Obviously they're going to ascend the technology tree quite quickly
Fundamentally incorrect. Knowledge is only one half of the equation, the other is industry.
Take the most primitive, rudimentary steam engine. The boiler needs to be constructed from relatively strong material in order to withstand the pressure inside it. You can start with lead and bronze, which are easy to mine and refine ("easy" being a relative term, given your lack of miners and high-tech refining processes) - but they're weak, which limits the pressure the boiler can sustain, which limits the amount of work the engine can do based on the amount of fuel it's provided with.
Since your human population is small, they don't have all day to spend collecting fuel, so they'd want to optimise the boiler for higher pressures by using iron and steel. Except that to make high-quality iron, which you absolutely need if you don't want your boiler exploding, you need a blast furnace which is nontrivial and requires a lot of fuel and babysitting. To produce even higher-pressure boilers you require high-quality steel, likely via the Bessemer process - which requires the construction and operation of a Bessemer converter. Again, nontrivial.
In other words, you can't get to high-level industry until or unless you have the population and supporting lower-level industries to enable that industry. And high-quality steel, which is effectively required to build steam boilers with enough capacity to make them useful, requires a LOT of industry. This is why iron- and steel-making were small-scale, specialised industries until two centuries ago: it wasn't that people didn't have the technology, it's that industry to enable the technology didn't exist, and therefore nobody bothered thinking about it.
Your colony has that technology, but it doesn't matter. They can't build it until they have the industry to support it, and to build that industry is simply not possible with 300 people; it's going to take generations. Especially when the colonists are going to be spending most of their time building and foraging and raising children and defending themselves from wildlife.
Assuming they don't all die, that is. We've eradicated smallpox on Earth, but your colony world probably isn't going to be so lucky. How are your colonists going to deal with a disease that has a 30% mortality rate? How are they going to deal with new diseases that human medicine has never encountered?
The whole Eden/"start afresh" scenario really can't work unless you have a LOT of people to start with, or you're willing to accept that your new society is going to slip down to 11th-century levels within a few generations. If you're lucky the knowledge they have might enable them to get to the 21st century in 500 years instead of 1,000, but it's not going to be quick no matter which way you look at it.
Oh, and I hope your computers containing all that knowledge are durable enough to still work after that amount of time with no maintenance...