The Z motor must have been moving a bit though for a cut program of that length in time...I can't imagine that it was at the same depth for 2.5 hrs?

But yes motors do get hot when stationary as current is still passing through them to keep their position locked & stationary.

As for the Z axis being off....there could be lots of reasons - something in the code that you missed, something mechanical in the Z drive train that could cause it to bind in one direction, interference in cabling could cause dropped steps...& probably many other things as well.