The ambassador character is probably the most indicative of the Culture as a whole.
I would say your concept fits the setting quite well, actually, but it's up to you whether or not you like the mechanics you've got. You can always skew the other way, and let the mechanics you want shape the character. You don't necessarily have to be a scholar to be invested in 'dead rights' in your society. There could well be others who've had their consciousnesses uploaded digitally, who are now finding themselves being treated as property rather than intelligent beings.
Look To Windward and Surface Detail both deal with the idea of a digital afterlife-- it's an important background element of the former and a major part of the plot in the latter. If you were interested in reading more of the Culture, those would be my recommendations for you, based on your current direction.
If all three characters were from the same corrupt society and trying to escape it, that would be a pretty cool starting point-- a more contemporary earth-like civ, maybe a dystopian near-future society still limited to a single solar system. The Culture could linger on the fringes, subtly manipulating events as they often do. Given all that's apparently going wrong, perhaps even at this low technological level there's reason to intervene even if there's no real danger to the greater galaxy at this point.