and I still maintain that the tests show there probably is a noticeable effect.
You can't. Not with any measure of statistical confidence. At all. You might as well @#$ pull a few game results or go off of memory

.
TMIT, I think you're wrong to put so much emphasis on space victories when considering the impact of representation. Faster tech rate is important for any victory. The AI can choose to use its tech lead to build a spaceship faster... but it can also use it to fight wars more successfully, or defend itself on the final-stretch for a cultural victory.
A couple problems with this line of thinking:
1. The game is designed such that the later you go, the more you can get away with being technologically backwards. For domquest, slowing down the tech pace makes these victories EASIER to accomplish SOONER...at least if leveraged. If the smaller, more advanced civ gets mechinf it might slow you down a bit. But if you have 2x their production from earlier wars and the global pace is slower, what do you think happens then?
2. Culture and technology are SOMEWHAT at cross-purposes.
3. You can argue that, with space wins being so rare, that the tech pace is actually too slow already. When you think about it in practical terms, it is always the slowest victory condition (barring time) in optimized play.
When you drag tech pace into the mud, you're stealth buffing military. In civ, military is already king.
For example, in game #1, the +2 game ended during a massive war between the two remaining teams. One team managed to launch their spaceship during the war and that's what ended up winning it. In the +3 game, that same war just didn't take so long - because one team already had a significant lead.
People who visit the chiropractor are more likely to have severe fractures. Thus therefore thusly you can conclude with the same logic you are applying that visiting a chiropractor increases the risk of attaining a severe fracture. In reality, people who have severe fractures are just going to see the wrong person, but we don't care about reality.
That analogy applies perfectly to quoted example. When we ask "did this AI run away due to representation" the answer is almost a resounding "no". When we ask "did this AI run away because it was able to gobble extra land early in the game for some reason" the answer is "very likely". It could be as simply as a neighbor picking a different expansion priority early on and losing out on 2-3 city sites to a monster, then becoming a peace vassal and trading techs for 1000's and 1000's of beakers late game at a "friendly" status. There is absolutely no way in @#% rep can touch that. Not even for a second. You can keep up with immortal tech paces with 500

/turn with a few vassals.
I feel that with the +2 version I tend to see more variety in civic choice, and less tech-heavy end games.
Doesn't this conflict with the assertion that most AI choose US regardless of +2 or +3? If you claim it offers more variety among human players, do you have an actual method of tracking that? You still haven't even demonstrated that it's materially better in human hands in a majority of cases...I'm not sure it would be possible to do so.
I don't want rep to be the 'default' civic choice. I want it to be powerful, but situational.
The reason I'm here is to provide some perspective on how high level players game the unmodded AI. There are a LOT of immortal and deity games on this forum where the player *never uses representation*. They might jump straight to US, or in some cases (mids captured) police state. Any cottaged empire will favor US strongly. Any war game prefers police state when available (global bonus to military production and reduced war weariness at a point in the game where production > tech is a boon). I am arguing that it is only an instant "default" choice in the late game for weak players. There are times where it is useful and times where using it means that one isn't playing optimally.
Basically nerfing rep is like nerfing caste system, pacifism, or free market.
2. Is it possible the Ai uses espionage more, in no tech trading allowed, to steal more techs from each other?
(still trying to account for the fact I lost 10/10 of my last no tech trading allowed games, and easily won my next "no tech brokering" game, both on emperor difficulty)
Make the AI use counter-espionage missions and all of a sudden tech theft viability plummets. If they did that, they wouldn't want to use the slider to steal tech because it wouldn't be cost effective.
(because Specialists give weak yields compared to working actual tiles
Indeed. Even with +3 rep a raw spec is weaker than towns, railroad mines, workshops (with EITHER state property OR caste, and much weaker if both are active), environmentalism windmills, watermills of basically any kind, lumbermills, etc. If they're not pulling GPP that gets a great person, you probably have better alternatives especially if you plan.
Perhaps the thing that grated me most initially is the justification for nerfing rep. It wasn't nerfed because pyramids were felt too strong (a rational thing that would nevertheless be a misconception),
but rather to slow down late-game tech pace. Doh! But humans can still easily break 2k beakers/turn on these settings even without representation, so it's not going to slow it down much at all.
It just takes away one option among many to put up that kind of research. But why take away options on a perceived but inaccurate suspicion that rep is a central element in late game tech speed?
Put another way, I'd bet that if you nerfed US, you'd actually slow down victories MORE than this rep nerf *allegedly* did, because it's actually used more often. I stand by the assertion that if you REALLY want to selectively reduce tech speed late game,
just raise the tech costs of late game techs. I also stand by the assertion that this would be silly in what is already a war game where infantry + arty + anti tank + SAM can beat literally any AI stack combination in the game if nukes get banned. Seriously. I've shown that in earlier videos; infantry/arty roasting mechinf era troops alive (and losing WAY FEWER hammers than the AI while doing it too).