Repairing an EPDM roof is not that big a deal. You can try peeling back the roofing material so the repair can be made. If it is down too tight, just make a clean cut of the affected area, make the wood repairs, then repair. I have done this on two rigs. I have also completely replaced one roof - - you don't want to go there if you can make a good repair.

Check with a local roofing company that does "mono" roofing, normally a company that does a lot of commercial roofing material. Ask them if you could buy a small piece of EPDM large enough to do the repair (some of them will give you a scrap). If it is 3 x3, get at least 4 x 4 or better yet, about 4 x 8 and carry the extra with you perchance you argue with a tree sometime. (I always carry a repair section.)
Ask the roofer about glue suggestions - - you need a non-oil based contact cement. Cut the repair material to about 2" larger than needed for overlap. If required, be sure to lift any trims this material fits underneath. Coat both the roof area and the EPDM with the cement and let it get sticky. Carefully lay the material in place (be methodical and plan ahead - once it touches, it is down) and apply pressure. Then seal the seams and trims, etc with DICOR. Does not take all that long. The seams will be something you will need to watch for cracking since one will most likely be on the downslope of the roof.

Have fun,
Bob