Is there a quick way to square a swivel vise to the direction of
travel? I can get moderately close with a piece of paper and a piece
of precision rod stock. To get closer I have to cut something and use
a depth gage of some type horizontally to measure the difference from
one end to the other.

How about about tightening it down without it moving? I just tighten
a little and paper it. Then a little more and paper it again, etc, to
the point where I have to make final adjustments with a deadblow
hammer.

With one of my screwless vises I slap it on the table, square it up
with a machinist square, and clamp it down. I may have to make a few
hammer adjustments, but its already really close, and it doesn't move
enough to be noticeable when I tighten it in place with clamps.

Actually I so rarely need to use the swivel part of the vise I was
thinking about removing it from the mill entirely... maybe throw it on
the noname mill drill (if it isn't too tall or maybe with swivel
removed) and leave a pair of screwless vises on the RF-30 instead.
Take a little time to square them up to the mill and each other and
leave them on it.