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for example, the green 'P' shaped piece in the top left of the 6x10 grid cannot be rotated into place in the 5x12 grid, instead it has to be fipped over.
moocher-
So you want a set of pieces that can make up x × y rectangles without any of them needing to be flipped over?
I'm 99% sure that is possible based on the following "proof": For example you could mirror every grid vertically, so that the first set becomes a 6×20 grid. For the left hand side of the 5×24 grid you select all the pieces with the correct handedness leaving a mirror set for the right hand side.
The problem with that is you get duplicate pieces, is that something you want to avoid?
frankenbike
Can you explain that again?