Don't Know anything about Russia.
But I do know you can extend a 30 day Mongolian visa in Ulaanbaatar. I paid for just 7 extra days, but I believe up to 30 isn't a problem. This was last year.
30 days seem to be the length of the standard tourist visa, so maybe you'll have to contact a travel agent inside Mongolia to help with getting 60.
Having stuff sent out to UB shouldn't be problem. A good guesthouse should be able to help you out there.
It may not be part of your route, but, just to let you know, you can enter China through the (now open to foreigners) Bulgan border crossing in the far west Khovd prov. It's a good option for traveling on to Urumqi where Khazak and Kyrgyz visas can be got.
I picked up an Iranian visa in Dushanbe (with the help of a online travel agent)
Best of luck