I recommend that "surplus" research for the civilization be stored similarly to how "surplus" manufacturing is stored for core worlds and that it be usable to immediately complete as many technologies as can be completed with the "surplus" as long as the player selects technologies that can be completed with the "surplus" technology.  At that point, the game would wait to the next turn to add the new research to the "surplus" to see if there is sufficient research to complete the selected technology.

The first screen snapshot below shows the "surplus" manufacturing that has been stored for one of my core worlds.  It is available to be used when I request that something be built on that world.  However, I recommend that the "surplus" be allowed to be used to build as many improvements in the next turn as can be built with the "surplus" and the manufacturing generated on the next turn (this is related to,  but not my main recommendation). 

The second screen snapshot shows that, in my current game, I am generating over 7,000 units of research per turn.

The third screen snapshot shows that my next selected technology to research only requires 563 units of research.  What I find annoying, and I think should be changed, is that I will only use the 563 units of research on my next turn and the remaining 6,873 units of research that I generated will be wasted.  I should the game should be modified in one of these 2 ways:

1. be able to queue-up technologies to be researced and, each turn, complete as many of those technologies as can be with the available research, or
2. create the "surplus" research bucket as described above and let the player immediately complete as many technologies as there is "surplus" available

I think option 2 would be easier programmatically, but I leave that decision up to you.  The main point is that the game should stop wasting research that the player has worked to build up.