The route marked on the OSM that you are calling 'middle route' is the 'South Route'.
I can't find that border crossing you are talking about, but there is a road that runs from China, though to the village of Mankhan (about 100ks from Khovd) that joins the route marked on OSM, It is marked kinda on OSM but you will only see it at higher zoom levels. It is a actually becoming a major road as the Chinese are build a new road through here. You mention Altay which is the west of Mongolia so this may the road you need so I think you will need to ride up to this road from China border crossing.
Maybe PM Walter Colebatch, he may know.
Tashanta is not the one you want, this the crossing from Russia.
Worse case follow the tire tracks that head in right direction and ask the locals, if this is a multilateral border traffic to major towns (for want of a better word) will go this way.
BTW make sure you bike is happy on 80 octane petrol. It might all you can get in smaller villages.
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