while I have never attempted to use rebreather, the point of the 1993 UofBuffalo study did basically just that but in a controlled flume tank. They took extreme measures to ensure that each diver had enough acclimatization time that they could learn how to best use each fin. They used about 30 divers and tested 12-15 pairs of fins on all of the divers, some from the Navy's NEDU, some locals. It was a huge study that took over 6 months to collect the data. This study was sponsored by the Navy and from what I understand cost hundreds of thousands dollars (not sure, but >$200k wouldn't surprise me). I really wish that I had a digital copy of it to distribute.
I have conducted a similar concept study, the study (not scientific, but a solid attempt was made) was on a shore dive that myself and the 3 friends that I included in the study conducted on a well known dive site. We executed the same dive 10 times each (2 times with each of 5 fins). We did our absolute best to do the same dive each time (including reviewing depth/time profile on our dive computers). The point was to replicate the dive every time with all 4 divers swimming at speed the entire dive. At the end of the dive we measured PSI consumed and tank size, water temp to calculate SAC for each dive. I was the only Force Fin user at the start of the test.
The fins, were the Force Fin Pro, Force Fin Extra Tan Delta, Apollo Bio-Fin (not sure, but I think the XT) , Jets, and Volo Race. The Divers, included 2 expirienced (500+ dives), 1 intermediate (~50 dives) and 1 new diver (~10-15 at the start). It took us a little over a month to do, but the order that each person used the fins was varied so that we could eliminate patterns. The average swimming speed was high, intentionally too high to allow frog kicking, this also forced the breathing rates up enough that we could more easily observe the difference.
The results- The Force Fin Pro was the most efficient, by a moderate amount (5-8% better for all dives). The Bio-fin was second. Followed by the Force Fin Extra, although it was the best fin for me, it was way too stiff for the other 3 and their SAC suffered. The Volo Race beat the Jets, but not by much. The difference in the bottom 3 was really small, to the point that statistically they were equal.
As a follow on, I should look at repeat at slower speeds to allow frog kicking, although I expect that the results will be really hard to see as the differences will be so small.