After discovering my bed bracket was upside down it was time to correct that and try locknuts under the bed plate to hold the screws in place. A locknut is used in engineering to tighten against another full nut or a plate to make sure it doesn't work loose in operation.
Assembling the heated bed is hard enough without the long countersunk screws wobbling all over the place and trying to escape onto the floor. Not only that, if you are using wingnuts or plastic wheels there's always the chance that the screws will simply rotate instead of tightening or loosening to adjust the bed corner height. The only question was whether the springs would fit over the nuts, they do.
So - remove the heated bed, turn it over, catching the screws and springs, set the springs to one side and put each screw back in turn, but then spin one of the spare M3 nuts from the kit down the screw and tighten it up, repeat for the other three corners.
If your bed frame has holes in the right places, the heated bed should just drop back into place, fitting the springs as you go and then tightening up the wingnut before doing the bed levelling dance.