On SnakeShot2, I did see the imprecision you saw (it's not a monitor-refresh-rate thing, btw, but rather sim frame rate; once our game sends the bits off to the video card it honestly doesn't care what happens to them or when), but if I did something very similar but not as broken up:
<loop iterations="600" take_pants_off_head="true">
<change angle="10" relative="true" speed="0" time="0.20"/>
<wait time="0.15"/>
</loop>
It seems to work fine. I'm not able to see any shots getting demonstrably "out of line". Possibly they would on lower framerates. You could perhaps make the changes coarser to deal with it should that come up.
Anyway, in general our engine is floating-point based and not fixed-frame-length and so there are limits to the precision. If you don't want to hit them, don't try so hard
If you want pixel-perfect motion the location-based patterns probably do a decent job of that, though getting a smooth arc there would be excessively painful.