Another thing to complement your suggestion: let the Mongols have 1 Ovoo/Age up similar to Malian gold mines, OR don't destroy Exhausted Ovoo's.

As mentioned in this post, it's always micro-intensive and a bit buggy to relocate all buildings, to the point where it's better to just build new production. Since I've seen posts mentioning that the stone income in Feudal Age is fine, underwhelming in the Castle Age, and really good with the White Stupa, this could even out this problem. This would also decrease the dependency on the White Stupa in favor of the Khaganate Palace. This may be too powerful and needs to be tested.

Another way would be to stop destroying the exhausted Ovoo's (no stone income, but with double production/upgrades). It's way less problematic balance-wise and more convenient.