"Did India want this project to be entirely homegrown?"

I suspect so and I also think that if you are going to test your skills, then being realistic in the first place is good idea. The mission was always sold as unlikely to survive the night but that would be a nice to have if it did.

For me the mission seems to have worked rather well and performed exactly as billed.

Not entirely. There were plans for international cooperation for the missions (with Russia IIRC). However, it didn't go through. Anyway, future collaborations are planned - probably with Japan first.

Has any country exported an RTG to be shot into space by someone else?

Vertically-integrating it yourself is one thing, but I'd expect NASA exporting a chunk of plutonium to India, even if they're both are nuclear states, would be challenging.

the US supplies nuclear weapons to partner countries and keeps them in US custody and guard while on foreign soil. I suspect the same kind of agreement would be in place with an RTG until launched.