I would get a couple of boards up by whatever means, and continue using a reciprocating saw, to cut between joist and board, severing the screws.
The remains of the screw in the deck board could be punched out easily from the underside.
The joists could be removed, and any rot and screw remains could be removed running them through a band saw with bi-metal blade.
They could then be treated, and re-installed upside down.
This is a fair bit of work but, probably quicker than messing with screws, and a lot less tedious.
We have taken a few decks up, and just spun the joists over, as the customers didn’t want the expense of us tidying them up, even doing this, will give many years of life, depending on the extent of rot.
We installed a deck last year, it had aluminium posts, aluminium joists, and composite deck boards. It was finished with glass balustrades and looked really nice and contemporary but, didn’t have the character of tradition decking, and would only suit certain properties.
One thing’s for sure, it won’t rot in a very long time.
However, it did cost an absolute fortune.
I’m told they are developing composite joists and posts now. I still like a tradition deck but, not the rot or maintenance.