Research/Engineering split.
I've been hesitant to suggest something like this because it sounds complicated, but maybe it is not so bad in practice.
Basically: Remove techs that progress basic technology (like new power plant tech, or EM sensor level) from the current research list and add them to a new list for theoretical research.
Theoretical research would use a fixed pool of RPs that is not determined by research labs, only by other factors like scientist skill or anomaly multipliers. Alternatively, only a fixed number of labs can be used for theoretical research at any one time - 5? 10?. The RP cost of theoretical research would not escalate to the same degree as the RP cost of regular research ("Engineering"), because there is no expectation of an increasing # of research labs. A simple way to implement this would be to generate theoretical RPs automatically, and the player simply insta-buys theoretical projects when they can afford the cost. Mechanically, this is very similar, although perhaps it is not as strong for narrative purposes.
The idea is that even smaller empires can keep up in basic technology. Right now, larger is always better; more wealth, more RPs, more technology. With a science/engineering split, both the small empire and the large empire might have the same level of basic technology. However, the larger empire would still have a large advantage in engineering; it would be far easier for them to build large sensors, large engines, powerful jump drives, etc.
There are numerous basic techs that would still make sense as remaining in engineering, like colony cost multiplier or engine multiplier.
Missile Agility Bonus
Random thought: Missiles get a small % bonus to agility based on the number of missiles the engine has. This would cap out somewhere (8x?), but it would mean missiles arn't literally always better off with a single engine like they are now. There is a RP premium for researching single engines for missiles, but it is so small as to be a nonfactor IMO.