Approach: #11's proof in a mirror, from a different start

11 is a binary counter whose digits burn a unit of fuel each time a carry touches them, and its proof is an invariant showing that a digit only ever runs dry where that is harmless. #33 is #11's table in a mirror, and this machine is #33's table with the state letters renamed, started in the state that is #33's D (equivalently, #11 mirrored and started in #11's state C). So you see #33's counter, with the head at the left end, on a run of its own.

Everything in #33's proof except the start carries over unchanged: the two moves (add 1, and overflow), #11's invariant, and the proof that every move keeps it. What is new is a 687-step opening. In it the counter loses its digits to merges until none is left, an overflow builds a new one, and at step 687 the tape is a one-digit counter with fuel to spare, a state the invariant covers. From then on the argument applies, so this machine never halts.

The Rocq file is #33's with the states renamed and a new opening. It replays the 687 steps, checks the invariant there, and proves the result for this table directly.