I'd vote that it's a genuine convertible.
The doors are correct, and so is the windshield header.
It looks like the top has been fitted incorrectly, in order to give a bigger rear window area, so with the top up the proportions are all wrong.
The front screen height looks correct (it's 12" on the convertible/woody and 14" on all P15 hard tops).
The rear fender side trim is wrong. So are the hubcaps. And the sill plates.
There's also an extra piece of trim on the hood, under the ornament.
Also, the door garnish molding chrome trims aren't correct on a convertible.
So... quite a few extra bits of bling, but the front fender 'special deluxe' badges are missing.
It clearly needs a bit of work, but it's going to make a nice car for someone.
Happy bidding!
R.