If I may step in here because my CoreXY has almost exactly the same bed dimensions - 400 x 400 x 10mm thick tooling plate. I don't use any form of software/firmware bed levelling or flatness compensation because there is no need. If the bed is flat, it doesn't need to be compensated and if it's level and stays level, there is no need to adjust. Having started with a Mendel built from a kit, and having to do all sorts of compensation before every print, I can say that life is now so much easier. Now I just turn on the printer, select a file and hit print - the start gcode takes care of the heating and initial homing.
I'm not saying all this because of any desire to boast or brag, merely that you are in an ideal position to achieve the same results. If you use 3 lead screws (my recommendation would be to avoid course lead, multi start screws) spaced such that one screw is near front left, another is near front right and the third is in the centre at the rear you can lift the bed with a continuous belt and a single Nema 17. Trust me, it works. The screws should only provide lift and should not be used to constrain the bed. This should be done by using linear guides. You only need two - one at each diagonally opposite corner. To initially level the bed, I simply slacken the grub screws holding the toothed pulley on to the screw, and rotate the screws. This only needs to be done once when it's first assembled, then maybe once again after a few hours of use.
You might find my blog useful, particularly this page https://somei3deas.wordpress.com/my-corexy-printer-build/
HTH