"top off my UA MP account with the needed segments"

--hardly what I would call "topping off"

But great report. A gruelling way to earn 1K IMHO.

For next year, you might want to check out the Star Alliance forum with the RTW threads and some surmising how on a RTW LITE fare and very short flights between a number of city pairs, you might be able to do this sort of thing in North America!