Here is how I would use Tennant. I might have him as the clone Doctor, perhaps on his way to become the Valeyard. He is with Rose after all. Having him as a threat that Smith must overcome might be interesting.
In typical superhero tema us, they start as rivals/enemies first.
Turn it on its head, and have Matt regenerate as the battle concludes.
The metacrisis (Lord, how I hate that "word") Doctor has one heart, ages and cannot regenerate.
that whole Realdoll story.