[Menschenfresser]

Hmmm...
What about simply having a secondary effect of the MEE being that one race (not human) stumbles across some ultimate technology.

It would give them some of the following if not all and it could be random as to what they get so the human player doesn't know what he'll be up against when it happens. I personally would suggest having it random, but having several of these listed:
1) Unlimited resources. (wouldn't be too hard...just make a new mineral/organic/radio extractor that mines 100000 per turn....this would work if the AI upgrades facilities, which I am not sure of.)
2) Gigantic hull designs.
3) These super components and hull cost virtually nothing, so they can build 50 in no time.
4) Super mega death weapons. (Don't know exactly what this would be.
5) A thick small shield tech that makes fighters a greater problem to erradicate.
6) A combat and defense component making their ships extremely hard to hit.
7) Space yards which can construct 10000 resources in a turn.
....ad nauseum......

I am not completely sure it is possible to mod in more MEE like events, but if that is possible then the rest certainly is. It would only take some serious detail changes to the AI design files so they actually use the new tech in no matter what form it comes in.

I see it may be impossible to radomize the actual rewards for the AI or who it goes to, but with careful consideration what is chosen to implement could be balanced.

Imagine having gone through a WP several turns ago and just seeing the remnants of an empire you have been crushing for a decade, when all of a sudden, a terror fleet of yours reenters the AI's system on a routine misson of death and solar rape, and there, hovering over a star, are 75 warships weighing in at 2500k a piece, which the AI can spit out at the rate of one every turn or two.

And think then about the unlimited resource addition. Say the empire which has gained this tech is on the other end of the galaxy. All the other AI empires they are allied with in at least a tech swap will suddenly have near unlimited resources through trade. Furthertheless, destroying their planets won't do much to hinder their mining ability...needing only two of each facility to produce what your spralling empire is producing.

Or there could even be multiple levels of MEE tech.

Although all this sounds like there would definitely be hard coding involved.