It's not clear what you consider "a version of IRV", but here are some candidates:
- Coombs's method is very similar to IRV, only changing the rule of who to eliminate in each round. (Eliminate the candidate ranked last by the largest number of voters, rather than the candidate ranked first by the fewest.)
- Baldwin's method is kind of similar to IRV, with an elimination rule based on tallying the rankings. (Sum all the rankings for each candidate and eliminate the candidate with the worst sum.)
- Nanson's method is similar to Baldwin's. (Eliminate all candidates whose ranking sums are worse than average.)
- Bottom-Two-Runoff IRV is a sort of contrived variation of IRV that ensures that a Condorcet winner remains in the race. Instead of eliminating the candidate ranked first by the fewest, hold a virtual runoff between the two least-favorited candidates and keep the winner. (At that point you might as well just use a full Condorcet method and do all the pairwise comparisons in one round, though.)
- Likewise, there are other Condorcet-IRV hybrids which seem like a waste of time to me, since you might as well just adopt a regular Condorcet method at that point:
All of these would have elected Montroll in Burlington, but don't really match what you've described.
If "version of IRV" just includes any voting system with ranked ballots, then just skip all that elimination stuff and adopt a plain Condorcet method like Tideman Ranked Pairs or Schulze method. These consider all voters' preferences simultaneously and find the candidate who would beat every other in a round-robin tournament.