These 'Diall Annular ring nail' nails are very close to the nails used to hold down the chipboard: https://www.diy.com/departments/diall-annular-ring-nail-l-75mm-dia-3-75mm-1kg/3663602743705_BQ.prd. The rings around the nail really grip and make it impossible to remove the nail with a crowbar/prybar without cracking the chipboard.
"impossible ... without ... cracking the chipboard" - no its not. I, like thousands of other tradesmen and women, have been lifting all kinds of boards without cracking" anything for my working life. I was the first post to offer you advice my ungrateful pal. BTW: why dont you help yourself and post a few photos?
I just used this. Hammer the small end down and under the nail head and pull. Magnusson Pry Bar 8" | Crowbars | Screwfix.com There will be a little damage to the board but not as much as drilling a hole in it. I believe diamonds should not be used to cut steel due to its carbon content. I think it reacts with the carbon the diamond is made from. Probably you are just clogging them up with softer material than they are designed for.
Prying underneath is very difficult but I'll have a look. I agree that diamond holesaw cutters are not good - they wear out far too quickly and the diamond burns out.