I would not take Tech Sights estimates as gospel. I haven't precisely determined how much 1 click of elevation adjustment on my Tech Sight TS 200 rear sight mounted on my Ruger 10/22 carbine subtends at 25 yards but I am quite sure it is a bit less than 1/4" (1 MOA). But as you said, this adjustment will depend on sight radius. The newer Marlin 60s have barrels only 1/2" longer than the Ruger 10/22 with carbine length barrel, but I believe older ones before the 1980s or so had barrels several inches longer. And the Tech sights might mount at a different location on the receiver for the Marlin 60 than they do for the Ruger 10/22. And the magnitude of a one-click adjustment can even vary with ammo.
As for the Appleseed AQTs, I have shot at two 2 day events this year and around 12-14 AQTs all told. I have never seen an AQT target with the 1" black sighting square superimposed on the center of the silhouettes nor do I see them listed on the Project Appleseed store website. Are you sure that photo was not simply a demonstration of what the results of a 4 MOA level of shooter/rifle/ammo accuracy correspond to on an AQT with scaled D targets? The Appleseed non-KD events are generally set up at a 25 meter (not 25 yard) range unless using an indoor range limited to 25 yards. So I would zero your rifle and sights for 25 meters, unless you know to do otherwise. If you get your sights set up to consistently put 5 rounds into a 1" square at 25 meters slung up prone, I would call it good.
As you know, the scaled targets used by both the Army and Project Appleseed are scaled down versions of the "D" or "dog" silhouette targets used for known distance qualifications. The D targets are 26" wide and 19" tall. In known distance Appleseed AQTs or the Army full distance AQT this same target is set at 100, 200, 300, and 400 yards. The D target silhouette corresponds to the black portion of the silhouette containing the 5 and 4 scoring areas of the reduced targets. As for how to adjust sights, I have always used a center of mass hold. These days, my eyes usually require me to use an optic anyway, and with a scope a COM sight picture is the only reasonable option. With iron sights, I can certainly see the advantage of a 6 o'clock hold. But the disadvantage I have always seen with that sight picture is it depends on the size of the bull at a given range and does not translate well to different size bullseyes at different ranges, which seems to be what you are wrestling with. If you really do prefer a 6 o'clock hold, I would zero your sights to use it on the smallest, 400 yard scaled silhouettes, then use a higher hold for the larger silhouettes. You probably can use nearly the same hold for both the Stage 3 rapid fire prone, and the Stage 4 slow fire prone, but you will definitely need to use a hold-over for the 100 and 200 scaled targets.
I would most definitely not attempt to adjust your sights between stages. Some shoot bosses will run the AQTs at a very rapid pace such that as soon as "cease fire" is called on one stage, and the line is cleared, the prep period for the next stage begins. And some times the prep period is so short that between "cease fire" on one stage and the end of prep for the next will allow you just enough time to prep magazines, sling up, and find your NPOA before the "load" or "fire" command is given. In that type of case, you simply won't have time to mess with sights.
Another issue is what position on the silhouette you chose to be your intended point of impact. Some AQTs are scored on a "hits count" basis where any hit within or touching the black counts as a "hit" whether it is in the "5" scoring zone or the "4" scoring zone. A hit that does not touch the black in the "3" scoring zone does not count. Some shoot bosses will invoke the "thirty caliber rule". Since Project Appleseed shoots were initially commonly shot with 30.06 Garands (and sometimes still are) and a .30 caliber hole is a little bigger than a .223-.225" diameter hole, a hole that just barely misses the higher scoring area will be ruled as hitting it so as to make the scoring caliber independent. But some bosses will not invoke this rule, at least if they feel you should not need it, and especially if everyone is shooting 22LR. If you have square or round bull the decision is easy, you make your intended POI at the exact center. But if they are using 0,3,4,5 scoring, the decision is a bit harder with the irregular shape of the silhouettes. If you want to maximize your chances of getting a hit on the 5-point scoring area, you may not want to make your intended POI at the center of the "V" scoring ring. If you look at the center of that "V" ring, it is much closer the the bottom of the 5-point zone than it is the top or the sides of it. It is even a bit closer to the shortest distance to the "shoulder" portion of that 5-point zone. So I will usually aim to try to hit near the top of the V ring circle on a 0,3,4,5 point silhouette, or right around the level that corresponds to the outside edges of the shoulders of a uniformly black D target. But you gain more leeway in windage if you sight lower, so this might depend in part on the orientation of your "wobble zone" and whether it is oriented more vertically or more horizontally.