I've got a lot of experience with plastic heat forming but have never welded it. I watched a guy weld plastic once. Did a good job. You've got to have some experience, of course, and just the right "touch". And a heat gun with special attachment or plastic welding gun which is just a specialized heat gun. Then you get plastic rods of the correct substance for what you're welding. I don't know what our scoot plastics are made of. (Polypropylene?,Polyamide?,Copolymer?,ect?)
Anyway, you could get all the equipment and stuff and learn how to do it for not a heck of a lot of money (maybe the cost of one nice new plastic piece.
Even then, it may not work out well at the screw down points as the weld might have irregularities that have to be ground flat. Still, it does open up a lot of possibilities.
Depending on the particular damage, if it were me, I'd probably try to use a washer under the screw head if possible.