You don't have any plans at all? South Korea is nice, but I would think you would have a rough idea if your spending 2 months there or 2 weeks. And like I said, if you're not going to make any detours, the east of Russia is pretty straight forward.
What you could do is just get a Mongolian visa in your last week before departure. And if it happens to run out, you get a new one in Ulan Ude.
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2011 Overland from Amsterdam to Nepal and back
2018 Overland from Amsterdam to Tokyo via Central Asia and Mongolia
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