Brilliant idea, very similar to what I thought when I looked at endogenous growth literature.

First and most importantly, the mod should delete the empire size penalty on tech, because in our mod we use diffusion to close the gap between snowballing player and AI, and the size penalty was introduced to address the same problem.

5 year interval is great idea, which corresponds to some "quality ladder" of tech diffusion. What I thought was like the tech one empire could diffuse is one tier less than its current level in three fields respectively. But my idea is too complicated to implement.

Peacetime: I think the idea to have a pairing is not good. You could fall into the pitfall of stacking more AIs to get more bonus, even though you have the upper limit of 6 times of your own production (this 6 number is also too much, just think about how fast you learn in a school, even with textbooks and lecturers). My suggestion is to first calculate all possible influencers for the given empire and form a "tech donor pool", and take the maximum (or max 2, max 3 as you wish) in terms of research points of all influencers as the source of the bonus. This becomes more plausible. For example, it is hard to imagine who else you can learn from when you are already learning from fallen empires.

You should also simplify the rule for multiplier: relations should not appear in calculation, retain only open border and having embassy as the sole conditions except treaties. Neighboring is not important, as we see in game communication is real time across galaxy. Treaties have good bonuses, but the multiplier should be max operator, not stacking up (taking sum). Otherwise there may be balancing issue because players have less influence points production and thus can maintain less treaties than AI. Federation also have some rules, and should be stronger than treaties combined (if you stick to summing rather than max operator).

The effect of war is not perfect, as player can set war with fallen empire, build some fortress world to take bombardment for years, and get massive tech bonus at the same time. More importantly, the debris you have in space combat already provides means to study tech. My suggestion is to add some flat research points to each debris field, or set military ships to generate research points while in combat, so that you can still gain tech even though you lose the battle. Meanwhile, the open border in truce also affects the donor pool of an unwelcomed empire, which balances to some extent.

The role of espionage can also have an effect! We can have some operation that increase the multiplier, or adding a closed border country in the donor pool with a specific multiplier. However, this operation is not guaranteed to succeed, which is fundamentally different from other operations in vanilla game.

We can also set specific rules about who is excluded from donor pool. For example, the donor pool of an empire only consists of empires that are no more than "superior" in technology. This effectively excludes fallen empire going into the donor pool in early game, even with scions origin or what. I would say this is because it takes time to learn knowledge and it must go systematically. You simply cannot learn advanced math before you fully understand calculus.

Enigmatic engineering: the effect of this perk is controversial. We can simply define it as excluding the empire from any donor pool, so it becomes a must if player want to go far ahead. But realistically I would say the better definition is subtracting some flat value from the multiplier, or maybe give an additional 0.2 coefficient to the multiplier, so the tech diffusion is completely stopped or slowed drastically.

Overall this mod is great. The main issue I see is that you use a lot of summing and multiplying, but I think taking max operation effectively reduces the chance of "exploding numbers". I have an idea based on tech tree, where tech diffusion could be modeled more specifically, but this one is definitely a brilliant, elegant and less computer demanding idea to model the tech diffusion!