Classic plastic piece here - Bic Veloce. Bottom has been beat and scratched over the years but is otherwise still a great board for me.
I'd like to fair the bottom scratches, some of which are a mm or two deep. Any recommendations for the right material and method? (I have some experience with fiberglass repairs for boats.)

I think the product plus sandpaper used, would be worth more than the board. So I wonder why...
Nothing sticks quite as well to that material as it does to 'normal' epoxy boards, but it will be OK to treat it as if it were epoxy. Clean well, fill with a UV stable epoxy and q-cell mix, then sand.
Classic plastic piece here - Bic Veloce. Bottom has been beat and scratched over the years but is otherwise still a great board for me.
I'd like to fair the bottom scratches, some of which are a mm or two deep. Any recommendations for the right material and method? (I have some experience with fiberglass repairs for boats.)

A plastic body filler will work with those boards. I've rebuilt fin boxes in that vintage before using epoxy resins. Plasti Bond was what I used, just clean the surface really well before
For smaller scratches, sanding primer. A few coats with sanding in between will keep you from having to do a lot of putty.
If it's really extensive, maybe easier to find a newer board in better shape as Mark_australia suggests. It's not only the time/cost savings but getting a newer design may be the catalyst to improving your sailing. There are reasons that boards in the last two decades don't look like Veloces (I had a 278 and rather enjoyed it but the newer gear is easier, more range, etc. etc)
Maybe use a razor blade to trim/scrape off any high ridges on the sides of the deeper scratches, but otherwise I would leave it alone unless it was leaking. Not sure you will feel any difference after repairing.