You are doing a great job with the Eagle! I know you and the kids are ready to hit the road.
The ceiling was the first thing that we did in this coach. Everything was removed from the ceiling including the insulation and any tubing was filled with spray foam. We then put in 1 1/2 inch roofing insulation and filled any voids with spray foam. Then it was lined with 1/4 inch plywood. For the curves we chose to cut 3 inch strips from the plywood. I heard so many horror stories about the glued vinyl and I had seen this type of installation in another bus and liked it. It has been so many years ago I do not remember all of the details, but we found the vinyl at a local cloth store and it had a 1/8 inch foam already glued to it. It was wide enough that we could split it to make 2 strips for the ceiling.
We started in the back with the first piece facing up and screwed a 1/8 inch X 3/4 inch aluminum strip to hold it to the ceiling. This piece was then wrapped around the aluminum strip toward the front of the bus. We had premarked with a chalk line where the vinyl need to be stretched to and in this way could get a consistent width to the front and also hopefully eliminate any sag. The vinyl was the stappled along the front edge. The next piece was stappled facing up on top of the first piece and another aluminum strip was screwed on top of that. This process was repeated to the front of the bus.
Not all that difficult until your fingers are aching from trying to stretch and hold the vinyl and your neck will not move from looking up for so long.