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There are some more specialised tools for grinding surfaces that include dust extraction. Festool do some. I've never used them due to the cost, I doubt you could make it pay for such a small area.
You could cut an inspection hole, find the joists and cut alongside them through the adhesive using a track saw with dust extraction (the blade would suffer though). You would then be left with a much easier job levering with a crow bar and spotting the screws, or use a multi tool with a carbide blade to cut through the screws between the board and the joist.
Airhead-
Bearing in mind the alternative is a £5-7k labour bill..! Realistically though, I think the rip saw from work will go through it like butter once the tiles are off. Just depends how the top layer of rubber behaves with the SDS. You've reminded me that I cut through some of the side panel screws with a bolster chisel and lump hammer.
The rip should also make light work of the stud framing which is currently in the wrong place.I have a circular saw already but a track saw is on the cards if I have to install wall panels or cut any large boards. I could literally take a month plus off work and spend thousands on tools and we'd be better off...
Dramatic_Hammer
I’ve got the cheapo Titan one, good tip on the magnet - it was getting through the adhesive that made the most mess previously. Thinking about it, I could chisel along the support beams rather than all over but having seen the work elsewhere in the room, I doubt the screws are in a nice even pattern!