Had to give it a try... In the puzzle, I managed to do what you suggested, however, bear in mind I have a 2mm clearance between the puzzle and the box... to allow for glued up oopsies with the cubes not aligning 100%... a pitfall I found way back in earlier puzzles.
I went into Sketchup, placed the red piece in position and then drew a circle for the swing of the other two pieces. After moving it around in all directions it sort of failed at the extremes... I tried rotating then moving, rinse and repeat, but gave up. If I didn't have "generous" tolerances, I doubt it would work.
Having tested this... my 14 step vs 22 in the prior AKKU comment might also be a byproduct of generous tolerances.
If your first cut is too short... Take the second cut from the longer end... LBD
