Well, the front diff is really expensive to replace. It's unique to the Denalis. Ask me how I know, and it happened at a lot less than 250k.
At 250k, a lot of other major components are going to need replacing, if not now, soon - suspension, steering, hubs/bearings, etc.
A friend's son recently bought a 2011 Suburban with 156k miles for $10k. He's already thrown another $4k in repairs into it, and is still chasing a low oil pressure problem.
Lastly, the 6.2 is an aluminum-blocked hot-rod motor, not an HD motor like the cast-iron 6.0 in the 2500 Suburbans.
Now is not the time to be buying a used vehicle. But if it was me, given a $10k budget, I'd be looking older with fewer miles, even GMT800, maybe 2004-2006. Just my $.02