Brakes frozen then ok after reverse. Rain related?

Yes, the shoes could have gotten stuck in position during the wet-weather non-driving, and knocked back into position when you reversed.

If you have time and nice weather before the 120-mile trip, you might get out the jack and take the rear wheels and drums off, and just sneak some grease under the shoe edges where they touch the backing plate. You don't have to remove the shoes or undo any springs to do that; it's easy to pry a shoe away from the backing enough to sneak a screwdriver in with a blob of grease on the blade. Don't get any grease on the braking surfaces of the shoes or drums.

The shoes have definite little stamped areas on the edges that rest on little raised areas of the backing plate; those are the only places they touch, to be greased.

If your backing plates are rusty, those support areas probably stand out with a lighter shade of rust.

 

If I were you, I would inspect the condition of the brake drums inside.

Brakes are a responsible part of the car and you need to be sure that the brakes are in order.

I had a case when one of the springs on the rear drums jumped off, which led to the wheel locking.
It's good that this was not on the road, but near the house.
I inspected, installed the spring, added grease, assembled.