i am allmost sure it can be fifex , back in the eighties when i was still windsurfing the board were made of the same material.
and believe me i have had to fix my board more thene once.
i used a "glue"gun with special sticks. maybe a local surfshop (old school) can help you
Sounds like a good approach! Could try an adhesive approach first would be neater, and if that doesn't prove strong enough, perhaps try some brackets and bolt+nuts approach in discrete places where it won't show. Surely can't be that difficult to fix the two halves together!?
If it were me, because I live right ontop of a large industrial estate with 1,000s of small businesses specializing in all kinds of fields, I'd probably source out a plastic welding company and have it done professionally. I doubt they would charge much.