For a more "random" experience in the research area, maybe going into a different direction might be interesting to think about - whilst keeping a "kind of deterministic" system as it is now.
I personally really, really like that individual control you have over your ship designs. It's not like in most games: Destroyer Class I, Class II, etc. But that concept doesn't transfer to the underlying technologies you have to research. They are Tech I, Tech II, etc.
In todays military, if they for example want to have a new type of fighter, they compose a list of ideas, what that fighter should be able to do. Then the underlying research begins (if that is possible and in what areas new technologies or materials would have to be researched). I imagine a similar kind of system for Aurora without the actually given limits of certain weapons, ranges, etc.: You specify what kind of ship you want to have. In a second step the game then shows you a list of needed technologies for that ship type and what research duration each part would need (the duration would of course highly depend upon what you are actually capable of and the bigger the difference to your actual state of technology is, the bigger the duration will be).
You then go back and forth between design wishes and research list until you are happy with the individual research durations (maybe you didn't like the long duration of the new armor research and toned your wishes down to a "reasonable" duration) and give permission to research the modules.
That system would enable you to
a) react to certain situations individually (like in a war you realize that your laser weapons are slighty (5000km range) to short to overwhelm a certain enemy ship type, so you give a quick research order to increase the laser range and refit your ships quickly with the new weapon type; whilst in the actual system you would have to research the next (full) step of technology - which of course would bring your range 50.000km but would also need 18 month to research instead of 3)
b) give long term research jumps a go if your political situation allows for that in peace times
c) can control technology more precisely, be a bit more in control of your research time, etc.
Again, this would be quite an overhaul - don't know if it would be worth it.