Has anyone ever used drywall screws (the black ones for screwing
plasterboard - I think you call it sheetrock in the US- onto metal
studs and plastering over) for holding the strips in the right
alignment, instead of wooden dowels and/or plywood cleats, or is it a
really dumb idea? I mean just for those annoying bits where the new
strip won't quite line up over the one in place.

The screws don't rust as far as I know and as the whole lot is
encapsulated in epoxy afterwards I doubt if they ever would. I've used
them for fixing things into wood for years and never noticed any
detrimental effect, so I doubt that they would cause an damage to the
wood, assuming a pilot hole was drilled first.

It's just that they are so cheap and are so easy and quick to screw
in.

Another Pete