I dont think youll go back.to.50-70% farming, at all
There was a city. Cities have satellite towns and infrastructures. There are now a few hundred people. Conclusion, there's a hell of a lot of gear, storage, and prebuilt materials, laying around. Much or most of it will be protected from the elements.
The survivors will try at first to stay with what's easy and familiar. They wont choose mass farming or hunter-gatherer unless they feel obligated to, in the face of necessity/inevitability. They'll try other things too.
A group of a few hundred will have a wide range of skills.
My guess is, you'll see a society based on scavenging, and on safeguarding/stockpiling assets that can't easily be replaced like spare parts, generators and fuel. Some petroleum based fuels will degrade; others wont if stored carefully. Water can be separated even from the more volatile fuels (neat trick I once heard, Stephen Kings "The Stand" maybe?? unsure how accurate - add sugar: dissolves in water not fuel, water becomes denser and sinks, take the top 80% and it'll be usable).
I expect in the first few years, as they take stock and realise resources must be used sparingly, they will for example use horses to scavenge further out, or battery radios to communicate with outposts, but save fuel for key generators and key tools, not for heat and light. Medicines and cold dry storage will be important, food preservation will become common. Books with important knowledge will be crucial. That sort of thing. Teams will be established to find the key raw materials and safe places for them, and once basic survival is secured, teams led by those with past knowhow will set up rudimentary manufacturing and production systems to service cars and other machinery.
Why will they do that, and is it practical long term? Look at places like rural India and Africa, where there is a huge reliance on fixing up old machinery and cars, often decades old, and making them work by patching them. So I'd say, yes. They can and it'll work. They will discover that, when a useful item breaks and some mechanic says "I can probably jury rig a repair". They'll get very good at those.
They won't need to lose mechanisation because being several hundred people in a city they have enough resources and skills to.survive the immediate aftermath and live on local resources while they transition to.a scavenger society, which will keep the going long enough to transition to simple manufacturing and collectively organised small scale industry. There will be dozens to hundreds of places with diesel/kerosene/petroleum fuel storage, hundreds of workshops and engineeringechanics places..... I don't see them having any issues making that work, and that'll be the first thing they try. For example, you might not have microchips for modern cars, but you'll be able to find ways to make enough vehicles go (modding if needed), that it'll work for their needs. A city will have plenty of pre-microchip era vintage cars, or cheap trucks, or fork lifts, or other items, and their spare parts, in good condition. Ditto generators.
Your challenges are not difficult ones.
I think social issues (how they organise) falls under "best case", we assume they can organise in a way most are OK with. Or those who aren't, leave or die, or accept its their best chance anyway, or live in fear but obey. The city is more than big enough if they split into 2 or 3, and trade will be possible unless they are in a TV drama where everyone is irrational.
Food will in the first instance be scavenged and stockpiled, and later will be collectively scavenged and centrally rationed. Longer term they will need to produce food or hunt, but they'll have mechanised tools, and we can assume nature will reclaim so they can corall off an overgrown area and meat production is easy - salt/smoke and dry and you have winter food. Why meat emphasis? Its denser nutritionally, and far less work (keep them in a limited area and let nature take care of plant growth to feed them, and reproduction, 1 or 2 people per herd and lots of temp help at slaughter time), and they have the resources to support it.
Obligatory zombies - well, think how widely available munitions and fire, and defences, will be in a city. Scavenge at gun shops (US only), police stations, army buildings, or make your own crudely - bear traps, flamethrowers and soap based napalm equivalents... You just won't run out of supplies for those for a few years, and by then you'll find other solutions that won't run out. No problem.
Eventually stuff will wear out that can't be replaced, but the number of things that are essential to their present living will be small, and they will see it coming years away. Yeah, those lithium ion battery tools won't last as we can't fix batteries. We can stockpile a few thousand from houses and shops and industrial buildings, and charge them monthly, off generators and kerosene, and enough will last long enough to use their power tools for maybe 15-20 years. (I just bought a power tool with a 2014 battery, works fine). They'll run low eventually but with enough warning (years) to figure what they'll do instead. So time won't be as big a problem as it may seem.
Likewise living spaces. Yes houses and buildings degrade over years and decades, and eventually collapse, but not for a looong time. The masonry/concrete structures often last well, and you don't need to do much to prevent it or jury rig workarounds for the roof or timber windows that fail. So warm and dry spaces and storage are easy too.
Overall if they can work together, they should be okay.