There are absolutely no reason the CHT Nozzle causes this kind of issue, actually I am pretty sure the bed levelling would work without nozzle or with a stone in place of the noizzle, I would recommend you to go talk about this on this thread wich will be more related.
Changing the bed can make it too heavy, or make it grip somewhere, you may play with g-code to adjust current, but I am not sure this will even do something, or try another bed.