The thing that jumps out to me is that on ones where builders did affect positively, the Y-values were multiples of 4 without a builder, whereas the one with no effect was not a multiple of 4.
Good work!
This actually makes sense to me. In DOS, trigger areas, steel areas and blocker fields are all tracked in a map that has a coarser resolution than individual terrain pixels, instead it can only track in 4x4 pixel grid cells. It follows that other ports with very similar physics to DOS/Amiga would likely follow a similar implementation, and the fact that you observed a multiple-of-4 effect further supports this. So for example, in Fun 28, the "normal" exit spot at (87,64) actually corresponds to a 4x4 cell in the trigger map with upper-left corner (84,64) and lower-right corner (87,67). The "surprise exit spot" with builder at (91,63) would correspond to the 4x4 cell spanning (88,60)-(91,63), in other words the cell immediately upper-right of the "normal" cell.
It suggests that, perhaps due to a bug in how the game sets up the trigger map in Genesis, parts of an object's trigger area may be shifted horizontally one cell to the right from its intended location in the map, resulting in an effectively non-rectangular shape.
I forgot to take the trigger-map resolution into account when I suggested things to test. It's quite possible that the trick can work in other levels but may require more builders, as one builder may not be enough to take the walking path out from one grid cell of the trigger map to another. For example, in Mayhem 2, the "normal" exit cell would be (56,60)-(59,63) based on what you reported. The extraneous one would therefore probably be at (60,56)-(63,59). Since the normal exit location without builders is at y=62, to reach y=59 you'd need 3 build steps rather than just 1.
If my theory about bugs in how the game sets up the trigger map is correct, it's possible that the graphics style may not matter as much (similar effect may be available for the other styles of exits), but the direction of approaching the exit will probably still matter (since there's a fixed direction to how the trigger area gets shifted). [In other words, if it's not clear enough already, you may want to re-test the levels where you approach exit from the right, taking into account the multiple-of-4 effect and use more build steps accordingly.]
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Precise definitions wanted! PUC is what?
Sorry, I invented that acronym as shorthand for typing "physics update cycle". When talking about timing of things related to game physics, we can't use frames as the unit of time due to the lag frame phenomenon (for which the definition you asked about ["Is it an extra frame..."] is precisely correct, minus the fact that occasionally it may even be more than one extra frame). For lack of better phrasing, I'd use "number of times physics got updated or will be updated" as the unit of time when talking about physics, leading to "physics update cycle" and then "PUC".