The variant of IRV that doesn't suffer this issue is to simply check for Condorcet winners at each stage. If candidate A wins every 1v1 against other candidates, don't allow them to be dropped in the runoff.
that's less of a variant of IRV than it is a Condorcet method with a weird cycle-breaking rule. you still lose monotonicity with your weird rule so idk why you'd argue for this over any of the other Condorcet methods...
though: this does go the right way. Condorcet methods are worth discussion. IRV, not so much.
Because this one can be explained to normal people who seem to like the idea of IRV and voting reform but don't want complicated elections?
IRV gets implemented a ton in the US, surprisingly. It tends to get enacted because people understand it really quickly, and it tends to get repealed because of center squeeze.
It's a shame that's not what everyone uses :/