I use an Arkansas stone and typically a straight forward-and-backward motion, sometimes figure-eights with chisels.

Me too, but I use waterstones or wet/dry sandpaper for coarse stuff.
One alternative I read about somewhere and have tried a few times is to
hold the blade perpendicular to how you describe and sharpen so the
LENGTH of the blade goes front to back. Sorry, that's confusing - if
you were planing the stone, your plane would be perpendicular to the
stone - that's the orientation I'm talking about. Then hold the blade
so the sharp edge is flat on the stone with your left hand, and the
back end sticks up at an angle in your right hand. If that makes any
sense at all - I guess I need another coffee. Let me know if you want
me to try to clarify further. Anyway, for thicker plane blades, at
least, I've found it's easier to hold blades freehand this way without
"rocking" and getting a bellied surface. Or you can use a honing jig
and go front to back.
In short, I think it doesn't matter what direction you sharpen as long
as you end up with a sharp blade.
Andy