exceptionally interesting post, your mastery of this game is really impressive ... no idea how to solve your problems other than a feeling that preserving the horde & getting at India are the best options ... which don't make them at all feasible
On the problem of the hordes, here's my suggestion:
You take Budjak off the Ottomans, then occupy a line of Horde territoy up to the north (and maybe along the russian border) to prevent Bohemia et al to colonize all of their lands.
And then you hope they still deal with their armies so you basically just sit on that line of land, blocking any colonization. I don't know if that's too cheesy though.
Correct me if I'm wrong, but isn't the ability to colonize hordes restricted if you don't have a land connection between their provinces and your capital? I vaguely remember only being able to send colonists to inland horde provinces if they were within my colonization range - which could be a problem with a capital in London and lagging naval tech.
Hm, so he either has to move his capital (which is a bit gamey), or wait until a nearby province cores so it comes into range?
Personally, I'd prefer murdering the Peep... Bohemians. Let the ongoing GH war and (hopefully) weekness wars do the rest