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This isn't a computing hardware or software problem, it's an aerodynamics and propulsion, structures problem.

A team of engineering graduate students with a bit of funding might succeed, but the cost and custom hardware would be pretty high. The problem also gets more difficult as the rocket gets smaller.

Also, failed rockets are flying bombs, not something to be done lightly.

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It's also quite a challenging control problem, which at the end of the day turns into a software problem.

You can see what spacex (probably) does to turn it into a tractable problem for real time control in http://www.larsblackmore.com/iee_tcst13.pdf (Blackmore leads entry, descent, and landing at spacex).

My point being that the design of the control system is the hard part and the software implementation while not trivial isn't the problem being solved.

And the design of the control system for a small model rocket and whatever control authority can be created for it in hardware are super hard compared to however it is implemented.

Sure, I was just pointing out that control wasn't on your list - it doesn't fall under any of aerodynamics or propulsion or structures.

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