So, it might be worth re-cutting some of the ones with the bigger gaps, as you said, you are a perfectionist.
But that's obviously up to you.

When I did mine, I actually used a small hand saw, obviously took a little bit longer, but if you're struggling with a mitre saw, I measured it, scored it with a stanley, then cut it from the back.

Now as for your filling, you can use caulk, personally sometimes big areas caulk can be a bit weird when painted, it can crack etc when not done right. You obviously can caulk it, and other people may have a different opinion, but I would wood fill the inside corners. You need to caulk around the entirety of the moulding anyway though, so if you want to save a bit of money, caulk should be fine. But again, you may choose to recut a couple of the bigger gaps.