I am looking into a similar issue on my Jayco 23B. I found a pretty close match in stock at Windsor Plywood. The stuff was about $35 per sheet, and had matching batten style molding like you show in your picture to cover the seams. Unfortunately I see the closest Windsor store to your location is Thunder Bay!
I also found similar material at our local RV store in their giant desk catalog. Unfortunately they were quoting ~$90 per sheet, but sounded like they could get it. No samples in stock though, so can't really assess the match to your existing material. It was the RV store parts rep that put me on to Windsor.
I think the material to look for is called 1/8" luan (or lauan) plywood; we usually call it mahogany ply in the Great White North, but luan / lauan is a common term in the 'States. There is a line of this board in 4' x 8' sheets with the headliner material attached (in various colours and textures). Try a really good plywood supplier in your area; I didn't see this at Home Depot or similar.
Not sure of your roof construction details, but mine is the typical luan and Styrofoam vacuum formed panel. For the repair, I was going to use water based contact cement, that is compatible with Styrofoam. Jon Eakes recommends LePage Pres-Tite Green for this application.
What glue will stick to what?
Couple of other thoughts. Was going to use this type of saw to cut the existing paneling if I could get away with a patch
The RV tech that looked at our roof & ceiling used one of these to determine how far the moisture has spread behind the head liner material. It was wet over a considerably larger area than the apparent wrinkling. I also thought this tool would be good to assess when the roof structure was adequately dried out prior to installing new material.
Haven't done the job yet; just trying to figure out the scope and see if I can DIY or need the whole roof removed.
2006 Jayco 23B