Consider flat-tooth rip, TCG, or hollow-ground blades or even ATB+R
combination blades. They all have something other than just
opposite-angled teeth.

Agreed. The centerpoint of the tips of every other tooth, on the
blades you mention, are off-set to one side of the plane of the blade
body, and the other teeth's centerpoints are off-set to the opposite
side of the plane of the blade body. In essence (the essence I was
trying to convey), they are as angled teeth are, and that off-set
allows for the same function as the angling of teeth, to cut for
clearance (so there is no burn) while cutting the board.

Position the fence square to the table and parallel to the blade, and
no other position.

Sonny