Ken: You will not be able to buy the tires in Monoglia. I have an R100GS here and have never seen tires that will work on this bike here (I've been here 4 years). If you want to put on new tires in Mongolia, you will have to either bring them with you, or have them send by DHL or FedEx. Those companies are both reliable and pretty fast to Mongolia, but expensive. If you plan far enough in advance you could send them by regular parcel post to be held for you at the main post office. That would be cheaper, but I don't know anyone who has tried it with tires.
A few of the riders I have seen come through had their spare tires tied to the outside of their side cases. It makes the bike pretty wide, but it also gives you some padding if you have to lay the bike over to do any work or if you drop it over accidentally.