I agree that the scheme I propose would fail under many interpretations of how time travel works.

I disagree that we know enough to say that Time has a tendency towards computational simplicity, or that Time-Turners protect you from it, or for that matter that a Time-Turner chain is any more likely to short-circuit in some bizarre accident than a regular use of Time-Turners.

The simplest explanation I can think of under which my scheme might not work is actually the 6-hour buffer model. In that case, I expect no time travel would occur at all, so we'd want to design the scheme in such a way that (a) this is a clean way to fail and (b) this is not a failure case we expect short of either the world ending or the scheme not working.