For example, for the 12.5°, 15° and 20° ones, replace the two blocks in the top layer by the construction used for the top two blocks in the 25° record.
Also, I think “A lone upright block tips over at 11.3° in its thin direction” doesn’t imply “no matter what you do to the base, you can’t stand blocks up vertically at high tilts.”
I would think you could sneak in cage-like structures like these (seen from the top)
ABB A
A D ABB
CCD CCD
D
with blocks A and D taking most of the north-to-south loads and B and C taking most of the east-to-west loads.
Possibly that will only work near the base, where there is more pressure from above that prevents these blocks from falling over.
Possibly, such a construct with only three (at 120° angles) or two blocks could work, too.
Rearranging blocks at the top to make them taller shifts up the center of gravity for the entire structure, which can destabilize lower levels. So copying part of a more stable tower into a less stable one won't necessarily be an improvement.
Can’t some of these easily be improved upon?
For example, for the 12.5°, 15° and 20° ones, replace the two blocks in the top layer by the construction used for the top two blocks in the 25° record.
Also, I think “A lone upright block tips over at 11.3° in its thin direction” doesn’t imply “no matter what you do to the base, you can’t stand blocks up vertically at high tilts.”
I would think you could sneak in cage-like structures like these (seen from the top)
with blocks A and D taking most of the north-to-south loads and B and C taking most of the east-to-west loads.Possibly that will only work near the base, where there is more pressure from above that prevents these blocks from falling over.
Possibly, such a construct with only three (at 120° angles) or two blocks could work, too.
Rearranging blocks at the top to make them taller shifts up the center of gravity for the entire structure, which can destabilize lower levels. So copying part of a more stable tower into a less stable one won't necessarily be an improvement.