The problem with the XC is that it’s just not rigid enough, has too much flex, and needs to be handled delicately. Changing bits requires even more tender handling so you don’t move things around.
One solution between changing bits is to record your original bit starting point using G28.1 or G30.1. After you change bits, re-home your machine, then issue a G28/G30 to put you right back to the original starting carve position. Your XY will be accurate, but you’ll need to re-probe the Z depth for the new bit.