The idea of voluntarially driving up the AI progress to build a golem kind of goes against the entire point of the game I think. The game is designed to reward cutting as many corners and being as smart about lowering AI Progress as possible. Being put in a situation where you can drive the AI progress up by a huge amount for a big risk is an interesting idea but, at least for me, I don't even give it any thought because the mindset you're supposed to be in makes you do the evaluation "can I avoid doing this in order to keep the AI progress lower", and almost always I come to the conclusion that it's better not to touch it. If repairing the golem were vital or important I would consider different but when you play the AI progress balancing game, unless the golem somehow were to allow me to instantly win the game, I wouldn't really give it much thought and avoid capturing them if possible.
But there's other ways you could make the golems a convincing risk without involving AI Progress. I thought of it for a bit and here's my ideas.
1) The AI perseives the golem as an immense threat, and will make every attempt to stop it. In this regard, the golem functions like a reverse raid engine. A golem under player control will cause the AI to launch waves against a system the golem is in every couple minutes from a random adjascent system (lets say the highest level one). If the golem isn't adjascent to a system with a warp gate, nothing happens, so it's possible to get a break here by retreating the golem or by destroying warp gates before capturing the golem. However, if the golem moves into a system with an adjascent warp gate, the AI will again begin doing waves.
2) The destruction of a golem gives the AI a huge boost in confidence, or whatever passes for artificial confidence (perhaps the belief that they now have the tactical advantage now that you are stripped of your weapon). The AI immediately begins preparing for an interplanetary assault against you. Additionally, ships in the system where the golem was defeated, if the system is an AI system, become released from their post and are free to attack.