I can tell you that I wouldn't pay for a new rubber roof, ever. If you have to strip the roof to fix the damage, I would get a far superior roofing system like the flexarmor system.
Option B is to cut the rubber where the roof is soft (go 6 inches into solid wood to make your rubber cut). Repair the damaged wood substrate and cover it with Liquid EPDM material. https://www.epdmcoatings.com/liquid-rubber.php I did this on my old camper that had a soft spot in the back corner. The Liquid EPDM literally goes on like paint and bonds to the existing roof so you don't have any seams.
Option B would be far cheaper, and you might be able to do it yourself. I cut out the rotted plywood on the roof and cut the rotted sections of the 2x2 cross members out of the roof. I used Gorilla glue and screws to sister new 2x2's to the damaged 2x2's. Put some new fiberglass insulation in, put a new section of plywood down, "painted" on the EPDM and the leak was fixed.