Leaving bike in Mongolia is possible
Sorry to hear about the accident.
I don't know anything about leaving the bike in Russia but I'm currently in Mongolia and have met several bikers leaving their bikes in Ulan Baator for the winter and planning to fly back next year to finish their trip.
All these were being left at the Oasis Hostel (where all travellers meet in UB) and the process appeared to be the owners simply wrote a letter to Customs saying what was happening and you presented that when leaving the country. I don't know whether the owners charge for this but it would seem to be a fairly easy process. Oasis Hostel has a web site so you should be able to find the contact details with a Google search.
Good luck
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