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)

   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.