On Sat, 22 Sep 2018 14:57:58 -0700 (PDT), Mathew Newton wrote:

The membrane should be around 1-2mm thick and so I was intending on just gouging/scraping it away from the screw heads once located.

Find the screw, use a 1" hole saw with the drill just to side of the
screw. This'll free the sheet(*) leaving the screws and a nice handle
to unscrew them with (maybe...)

Or find the screw and use a screw extractor bit to remove the screw.

(*) The kerf might not be enough to make lifting the sheet easy.
Maybe two goes with the hole saw? First the 1" then a 1 1/2" this'll
give you a "kerf" of 1/4".

--
Cheers
Dave.