Hey QM,
Wow--that is kind of scary for us fishing types--mebbe you had better consider going back to mono instead of braid--or start targeting smaller fish!
I have almost gotten tangled up when a large redfish made a quick dive, but so far nothing big enough to do any damage. I don't know how compatible with the fin material it is, but there is a super adhesive that some use for yak applications called Lexel. Look into that, and always test these adhesives on a small area of the fin before going for a major repair.
Here is some info about it:
http://www.paddlerzone.co.nz/products/r ... el_sealant