While you're right that industrialisation occurred within 150 years for our modern society, it is important to note that the conditions which allowed for that do not necessarily exist in an apocalyptic environment. I personally think that the dark ages that would be brought on by an apocalypse would last much longer, possibly the 500 or 1000 year counts, not because society can't reinvent its technology faster, but because it can't reinvent its society faster.
During the industrial revolution, the vast majority of people in Europe and America could go about their business and travel through their country of origin in relative security. They didn't have to worry about their survival, so didn't need massive bands of mercenaries or soldiers to protect them as they moved about. This is important, because it means that travel costs a LOT less in terms of food energy, logistics, and the like. That means less farmers having to support people moving about.
Cities were even safer. Sure, there's the odd mugger about, but in 1729 Robert Peel creates the Metropolitan Police in London. This means that most citizens who spent a significant proportion of their day protecting their properties and lodgings with checking locks, etc. Now also have time to focus on other things, making them more productive. That means for the same amount of food energy, more gets done.
Village life and farming in general is safe, and the fact that countries have standing armies (dedicated military forces) means that people can devote their entire lives (even entire generations) to farming output, and the only limitations are land fertility, the climate and their farming practices, which if focused upon, can only improve. They don't have to worry about being called up at short notice to fight in a local battle at the order of the Manor lord, which not only distracts them but could also cut short their ability to produce more and share their knowledge and experience with others.
Finally, Gutenberg (2 centuries previously) has invented a simple method for mass-producing knowledge that can be shared cheaply with as many people who actually want it, provided you have paper manufacturing facilities, ink production and teams working on creating the typefaced text that is needed to print this knowledge out.
The benefit of non-survivalist thinking? A much smaller percentage of your population can be devoted to essentials like food production and military readiness, and the rest of your population are free to push knowledge forward through research and technological development. They can also do so MUCH more effectively because of the printed word.
Your apocalyptic society is a survivalist society. They have to produce food to survive, making food a critical resource in your society. Given that food must be produced on farms and land generally, food production is probably being done in a set region, which has to be protected at all costs. FAR more of your society as a percentage is now focused on food production or its defence, meaning that you lose the ability to conduct research to make your life better. Sure, one can argue that in the long term the research is beneficial, but Maslow's Hierarchy of Needs dictates that food production will have priority in a survivalist society, hence the research will not take place.
Clan based fiefdoms are a very useful political structure for low-tech environments as they don't require many of the advances (like writing) that we take for granted in the modern world. It's easy to know what the law is in a fiefdom; it's whatever the boss says it is. That boss can extend his reach as far as his enforcers can reach, but eventually scale destroys this model. Even Elizabeth I faced insurrection at least once from within her nobility. Believe it or not, the one thing that allows a country to unite on a large scale under a single banner that can manage said country effectively is Journalism.
Journalists are people whose sole function is reporting on the events of the nation (in this context). A heavy part of that is the political happenings. This works both ways; journalists inform the public of what a parliament decides, and it also informs the politicians on what the public thinks about that.
Rulers and managers require your obedience; great leaders inspire your obedience. To do that, they need to engage you in the narrative and explain to you why you need to pay so much tax and what its going to pay for that will make your life (or the life of your kids) better. These large scale systems of political (and by extension industrial) order are served by journalists who get those narratives to the people.
Your apocalyptic society that has devolved into fiefdoms not only doesn't need journalists, but actively doesn't want them. Anyone who challenges the chief is a liability and why are we feeding this person to be a gossip and sow insurrection anyway? It just won't happen.
Even then; let's assume that your fiefdom of (say) 50,000 people DOES have a fairly secure environment, food is plentiful and they are sufficiently remote that their army doesn't have to be that big. You might be able to engage in some form of research and development, and you may even have books that have survived the apocalypse to short cut the learning process. But to build a car from scratch you need a source of fuel (even coal if you're going for steam), an engineer, a blacksmith (preferably a boilermaker), and sundry other skills and ingenuity that are unlikely to form in a small environment, where breadth of skill is far more valuable than depth of skill.
Ultimately, what you really want to progress your science and technology again is safe travel of experts between domains, and a way for their knowledge to be shared between themselves quickly. This means organised printing presses, and a trans-domain market for books and knowledge. The afore-mentioned survivalist thinking will make this more difficult, but it can be achieved from a technical perspective.
From a perspective of society however, if all these fiefdoms are in competition with each other, why on earth would they just give away their most prized asset (information), especially when one considers how much of a percentage of their production it cost to generate it in the first place? This puts us right up against large scale political structures, or the lack thereof. In a world where resources are much more scarce than they are now, competition for them is much more intense and that means that the fiefdoms are not going to share readily. While it's possible that they may find a way to cooperate, they would only do so if their mutual survival was enhanced through such cooperation and transitioning from a survivalist culture to one that is less so isn't an easy transition as it involves the establishment of trust that things aren't going to go pear shaped again in a hurry.
Ideas MUST propagate easily for technology to advance, even in an artefact driven culture like Mad Max, where cars and fuel may exist, but the ability to repair / refuel / rebuild them has been lost. It is that 'cheap' transmission of ideas between parties and generations that allowed us such rapid advancement in the first place over the last 150 years.
During the middle ages, society didn't advance anywhere nearly as quickly as it did during the last 150 years. Part of the reason for that is tied to the conditions described above, but there is also a need for a foundation of knowledge to build upon in order to make great strides. For us, the Maxwell Equations (created by James Maxwell in the early 1860s) led to incredible strides forward in our theoretical knowledge and the ability to apply that knowledge practically in ways that were not possible without that particular knowledge.
In other words, there are certain pieces of knowledge that if we lose, will hinder our progress until we find them again.
The chances of the Maxwell Equations being lost is not very high, and our artefact rich apocalyptic society will probably figure most of it out on their own, but it's important to note that theoretical research is the bow wave of technological advancement; without certain theoretical knowledge, engineering advances simply are not possible along the lines that knowledge supports.
Your limiting factor in progressing from an apocalyptic society back to modern technology is not technological; it's social. It's clear that in all but the very worst apocalyptic scenarios, the environment for most survivors will be artefact rich, meaning that when one can focus on it, rebuilding knowledge and technology can occur at an accelerated rate by comparison to the original speed of development. It's the focus that will be the limiting factor. People will focus on their own survival first, then the survival of their group, then the protection of their group, then (as some technology re-emerges) on the advantages of working together at some form of 'national' level, and it's only THEN that the social constructs will be in place that will allow the survivors to leverage what they already have and know (as one) to develop more advanced industries and recreate the modern tools and information sharing abilities we currently enjoy.
Another way of putting this is that your society will begin to advance at the rate we have in the last 150 years when the people enjoy;
1) safe domestic lives
2) regular and consistent access to food and shelter
3) organised large scale government and industry
4) a culture of free knowledge sharing
5) an environment that encourages research and development, including the populace seeing regular benefits from such advances.
If we take the middle ages as an indicator, that could take a significant number of centuries to re-achieve. Until then, will alone does not an MRI make.