I might be missing something, but it seems to me like the way to modify to a smaller state diagram is to remove the HALT state from the TM and then redraw any state transition that goes to HALT to map to any other state arbitrarily.
This won’t change the behavior on computations that haven’t halted so far, because these computations never reached the HALT state, and so won’t be effected by any of the swapped transitions.
I might be missing something, but it seems to me like the way to modify to a smaller state diagram is to remove the HALT state from the TM and then redraw any state transition that goes to HALT to map to any other state arbitrarily.
This won’t change the behavior on computations that haven’t halted so far, because these computations never reached the HALT state, and so won’t be effected by any of the swapped transitions.