I think I know how to fix it. 
Your own fix was good but you forgot one thing you pointed out earlier.
You forgot to make it unknown to the Golden Horde aswell. As you said the countries in Europe just have to control the Golden Horde capital to know the way to Russia.
So maybe I should do something to it.. maybe split the horde and make the eastern Kazak Khanate. (This is actually historical but the two hordes were named white and blue horde.)
Your own fix was good but you forgot one thing you pointed out earlier.
You forgot to make it unknown to the Golden Horde aswell. As you said the countries in Europe just have to control the Golden Horde capital to know the way to Russia.
So maybe I should do something to it.. maybe split the horde and make the eastern Kazak Khanate. (This is actually historical but the two hordes were named white and blue horde.)