Thanks for the question.
Since you did not specifically mention what class you are flying in, we will cover all the bases.
I would guess that you are talking about Advanced class, since you mentioned autonomous vs. stabilization and you had what appears to be section 8 in your rule reference.
You are free to choose any flight stabilization system you wish to use for Advanced class.
If you choose a stabilization system that is capable of autonomous flight, please come prepared to completely document and explain how you have set the system up so that any autonomous flight feature of your unit is completely locked out of operation and cannot be used during the event. It might be simpler to chose a system that would not require your team to document that any autonomous features have been disabled and are not being used.
For other classes:
Regular class: No gyros or any form of stability assist or autopilot of any kind is allowed.
Micro class: Gyros, other forms of stability assist and autopilots are allowed, but you may not use autonomous flight.