Maybe the problem is that Barnaxus already does enough for golems, but that his in game abilities don't reflect his desire "to help (the Luchuirp) rebuild the Empire, to recall what was forgotten, and to perfect what was remembered... And the Luchuirp, amazingly, instead of rankling at being 'taught' by a golem, loved him back. He was their link to the past and an amazing store of knowledge."
Here's the idea - maybe Barnaxus should function like a reverse Loki and make a special building in the city he hangs out in which improves research and culture. That way, you wouldn't be grumpy over having Barnaxus parked in your capital, you'd be happy to have the extra beakers and notes. And tell me that he's not a) loads better than an Elder Council for research (since he cannot forget anything he ever witnessed) and b) a potent provider of culture, given that he personally witnessed the old Empire of Kradh-Ke-zun. Maybe +2 and +10%? I'd think he'd be worth more, flavor wise, but I don't want to make him horribly unbalanced. Perhaps just make him the equivalent of a Great Scientist and a Great Bard, sans the GPP?
It doesn't solve the "what if I never get him properly levelled" issue, and I also think he should be able to repair himself (heck, if he just got Enchantment I he'd also improve a little bit in combat potency which would make him easier to use in the early game without adding anything to his late game potency), but it would solve the pernicious feeling that he's sitting there doing nothing. It's also flavorful, in that he's far more likely to be educating the Luchurip than seeking combat once their empire is nominally secure. He's not, primarily, a warrior, but a leader and teacher.
My 2c.