I agree that these are the two factions that could use some substantial buffs, perhaps with the Tech Rebels lower level techs as well. But I think you're a little too extreme in some cases. Here's my item by item thoughts.
Compartmentalization: This ability reduces the cost of SB upgrades by 20%. I would suggest adding two things. First, have this tech increase the number of tactical slots at all planets by 5. Second, (if possible) increase the amount of upgrade slots available for each SB by 2. Increase the cost of the tech to compensate for how powerful this becomes.
Adding more tactical slots isn't bad. And while I think a tech should increase starbase upgrade slots, I think that deserves its own tech. If compartmentalization really needs more effect, just buff the cost discount.
Hardened Defenses: This ability adds 2 armor and +30% health to all tactical structures. I would suggest adding an ability to all tactical structures that prevents them from being disabled. This is quite powerful in the right circumstances but is not always useful. In addition, I would suggest making this a 2-tiered tech and reducing the % health bonus to 20% at each level.
Making them Kostura proof would be interesting.
Add a tech that increases the population level of all planets by 15%. This helps a turtling TEC player keep a strong economy as the game goes on and he gains fewer planets on average.
I agree what the loyalists need most in a substancial economic boost. However being TEC I think they'd do better from a trade buff.
Acclimatization of Will: 2 tiered tech; increases enemy allegiance change rates by 25% per level. This is a weak tech as it stands now. Generally, your culture is not strong enough to enact any allegiance change. I would propose increasing the rate boost to 30% per level and adding a 10% increase per level to your culture’s resistance to being pushed back by enemy culture
In theory this is actually one of their strongest techs. The problem is that its so easy to counter culture in advance with just a little of your own and cap ships. It could be better if getting around this were easier.
Buff Deliverance Engine to be able to overcome any culture generated by a planet (cause the planet to generate ~300 of your own culture/sec.) In addition, have DE damage the planets allegiance; maybe cut the planet’s current allegiance value in half (if this is possible). This would synergize well with Acclimatization of Will. To make sure this isn’t extraordinarily OP, lessen the duration of the culture production.
This is the big one. DE has never been very good. If it could disable culture at a target planet then perhaps culture wins might be a tiny bit possible.
That said, I think your tweaks will still be insufficient to make the Advent Loyalists competitive in multiplayer. At the minimum Unity Mass needs a buff and they'll probably need some super unique tech on the level of wail at least. Sadly I doubt they'll get it.