I looked into paying to have a TPE roof replaced and some wood repaired some years ago. I got numbers like $2600, $3300. I was at one dealer where they were replacing a roof and a lot of rotted wood behind the cap. I asked the guy how much that was going to cost and he said they had blown past $5000 and it wasn't finished. So, I went back to the DIY method.
If the wood is sound enough to keep the seams together and glue the rubber back down on the wood, you might be able to fix this with Eternabond tape.
I fixed some pretty bad leaks with this product. I once repaired a serious tear caused by a low hanging limb. It was a lot more ragged than your tear. Then and now I keep an Eternabond 'repair kit' in my trailer. I like the 6" white TPE and I use a lot of the 'double-stick' which does not have the TPE backer.
I now use Eternabond proactively at the seams at the roof rubber and the fiberglass cap. With good surface preparation it is about as good as the original roof.
it's not cheap and it takes a bit of practice to learn to work with this sticky stuff but I've found nothing better for roof repair and prevention. You need the Teflon scissors and a roller to activate the adhesive, maybe $40 in tooling.
They all leak at the seam between the cap and roof rubber. That's why I proactively lay down a 6" strip of Eternabond at those seams before it leaks.
Without knowing the condition of your wood it would be impossible to say for certain you might get away with a little new wood decking and Eternabond tape. But it's possible. If the wood will hold the screws it might work.
I had one trailer that had some soft spots but I was able to Eternabond tape over the area where it leaked under a luggage rack and never had another problem. It was just a little bit of a soft spot but as I said it never leaked.
I have also cutover from Dicor to the Eternacaulk. Stays cleaner and is more flexible. Price is about the same.
When I first began using the product I had some questions. These folks were helpful and know a lot about the materials we are dealing with on these trailers.
I know from personal experience how it feels to have serious roof leak or decaying wood. If you can get by without removing the cap, it might not be too difficult to fix. I hope you get it worked out.