Instant Runoff Voting (IRV) presumably would have behaved in essentially the same bad way in this election because this race was dominated by the top 3 contenders.
Top-2-runoff and IRV are the same thing in a 3-candidate race, if the voters are the same and act self-consistent. But how solid was the top-3 domination in this race? If 99% of Holloway's votes transferred to Roemer while only 1% went to Duke that would have (just barely) put Roemer in the runoff. However, a split that drastic would have been extremely implausible. Trying for the most-plausible scenario: If all candidates from Holloway (4th) onward were lumped into a single "supercandidate" with
votes, then in order for them to put Roemer into runoff ahead of Duke, those 124127 would have had to transfer 80652+X to Roemer, X to Duke, Y to Edwards, and Z failing to transfer to anybody, for some X,Y,Z≥0 with 80652+2X+Y+Z=124127. In practice in the real world, even in simple IRV elections with highly experienced voters, at least about 10% fail to transfer, so I think it is safe to assume Z≥12000. I also think it is safe to assume Y≥15000. Hence 80652+2X≥97127, hence 2X≤16475. So in order to push Roemer into runoff we would have needed a transfer from Supercandidate to Roemer of at least 88890 and from Supercandidate to Duke of at most 8237; this is a 92-8 percentage split. It seems safe to regard a split this drastic as having had virtually zero chance of happening. This completes our argument that IRV would not have changed the result.