First off I love the idea of more research options so I am behind this attempt to make that possible.

After playing a few games, to me it feels like with the random options the progression through the research tree is too slow.  and can keep you from play a game the way you prefer to play.  IE if you don't get a lot of ship upgrades but have a combat oriented race, you become unable to take advantage of your race perks.  Not getting the ability to have transports until turn 300+ is a real problem.  having the limited options is painful when the research time is over 5 turns.

So, it seems to me that reducing the time to research each tech could alleviate a lot of this pain, or as others have suggested a way to weight the options that show up.

I had a couple of thoughts on speeding up the research process other than just simply reducing the time it take for each one.  It could be that when you choose one tech to focus on... you also do 5 or 10% to all the techs that came up, so as techs pop up that you don't focus on they become shorter and shorter options to select.  Maybe cap this secondary research as 50% or 75% so you don't end up getting a free tech by ignoring it completely.  

I read the ability to have up to 7 choices would be able to be unlocked which might help, though it stoll doesn't address the issue of if you don't get the research projects you want, if they are all 5+ turns it is painful.  But moving the unlocks of the extra slots to earlier in the game might be helpful.

So far it  is a little frustrating to have a known problem and not be able to research a solution.  For example, being negative income per turn and not being able to research a new banking or trading tech.

Also in my latest game I have tried to take a research tech whenever it shows up and it has not greatly reduced my research time, though admittedly that may be my issue of not yet understanding how to take full advantage of the improvements I have unlocked.

At any rate it is my observation that if there are more techs to be added as development goes on a way to reduce or at least focus on a type of research should be added.