As a nerd, I automatically think of the travelling salesman problem
, although you don't have to return to the start. But you have other constraints (like scheduling Culebra), so it's not a perfect match.
As a hiker, I'll suggest that the hardest part Blanca-Lindsey ridge can be avoided by dropping into Winchell Lakes to the south. Getting from Lindsey to the Crestones might give you the biggest private-property headaches, but you might take a look at the Rainbow Trail as an alternative to going back over to the Sand Dunes. The path up Sand Creek from the dunes toward Music Pass is a beautiful hike (if you go that way), but you'll have to wade through the creek about 10 times, so plan your footwear accordingly.
Good luck! It sounds like you know the magnitude of what you're undertaking, unlike some of the previous "pre-announcers" that have Doug so ticked off.
Are you planning to post real-time updates? It won't be as exciting as John Prater's attempt, but I'm sure you'll have a lot of people interested.
Climbing at altitude is like hitting your head against a brick wall — it's great when you stop. -- Chris Darwin