Speaking as minor chemist, I am afraid there really is no need to run it bone dry to get rid of the 89 octane. It is a matter of dilution. If I have a 1/2 tank of 89 and a half of tank of 93, the new solution will be 91 octane. (Assuming they both use the same n-heptane and iso-octane that most places do.)
The two liquids would be a completely homologous and there would be no way to "extract" the 89 from the 93. It would be the same as mixing a 25% salt water solution and a 10% salt water solution. After mixing them, there would be no way to separate the two again.
As far as "sludge" in the tank. I again, find it hard to scientifically believe that there would be anything remotely noticeable after even a few tanks of 89 versus 93. Perhaps, if they are willing to pull in the CSI teams... but I doubt they are willing to go so far.
The one thing you mentioned that I had considered previously, was that the computer may record some secondary data about pressure reduction, etc., that occurred to facilitate the use of the 89 gas, that could be used to extrapolate the implied use of 89 gasoline. If they could use this data to show definitively that 89 was certainly, but not possibly used, they could have a case. I feel confident that there could be a number of explanations for changes in pressure, engine timing, etc., that would serve just as well as plausible explanations, freeing me from culpability.