If you're from the U.S. can't you visit Mexico relatively cheaply any time? If it's really a must for you, go, but I always say to see things that are harder to get to on your RTW.

Looks like a great list...and like you said, you can easily spend a month or more in each country. I was in Mongolia for only a week...wish I had a month! I really liked the part of China you are talking about. IMHO, much better than the rest of China. So far, I have spent about 6 months touring China...and want to head back to Yunan again for sure. Same with Vietnam....loved it there!
Next stops for me are Turkey, Kenya, Tanzania, Egypt and Morocco...
#9: Each of those countries requires a month also! What great places to visit...

A month in India will just be enough to get you started. But don't worry about that.
No one has mentioned Iran. I haven't been but I only ever hear good things. I also think Jordan and Syria would be worthwhile places to visit. I have only visited Egypt, Israel and a bit of Yemen, oh and the UAE and turkey in that part of the world.
I think you are getting propositioned because you are a westerner, not because of what you look like. Not so long ago in India I had a village guy running down the road calling out to me for "love". He chased me quite some distance. I was covered from head to toe and had sunglasses and gloves on as well. I am sure I looked hideous.