Forget the sprung Brooks. A regular Brooks should be fine.

Aero bars will be your best friend on long days with headwinds.

I assume that the hybrid is heavy because of a suspension fork? If so, you could easily have it replaced with a rigid fork and save several pounds. What else makes it so heavy?

If you look at a new road bike, make sure that you can fit the desired tires on it. A lot of road bike have very narrow clearance and cannot take very wide tires.

3000 miles is hard on any set of tires. I would pack a spare set for the trip.

It certainly sounds like a grueling trip. When do you depart?