[...] I'd like to set a stone that isn't flat-backed like the cabs
I've worked with before (all three of them - haha) and want to
have both sides of the stone open to be seen.
Do you want to set double-cabs, or even organic pebble shapes?
The comments so far seem good - and I also suggest you use thicker
fine sil for your bezel material and trim the height down - but
no-one's yet mentioned a spectacle eyewire-style (or coin bezel). As
I make spectacles I guess I have to chime in here It is a more
precise setting, so possibly not to your taste here.
more to your style is the free-form edge-wrapping technique using
fine sil that others endorse and which I've had a little success
For the spectacle eyewire-style setting, make the bezel wire from
strip stg sil and draw it through a half-round drawplate to make
channel of the appropriate dimensions to do the double-bezel job.
Wrap it around the stone and then decide whether to 1/ saw off excess
and solder on a closure device (like a little screw/nut thing that
spectacles and coin frames have) or 2/ curve the channel back and
around to make a little loop at the top. Solder the joint, pop in
the double-cab and wrap a bit of wire around under the top loop to
clinch the stone (this probably needs a drawing). I've seen some
victorian moonstones set like this with the channel looped at each
side, and connected together as a necklace.
The free-form edge-wrapping way is to use at least 0.5mm fine sil,
measure and solder to make a tight-ish bezel, then set it.
Unfortunately the bezel can grow in overall size during the
bezelling. You'll also find that when you push the bezel over at one
plece you merely succeed in putting a twist in the bezel strip. The
pliers idea someone suggested is one way of pushing both sides of
the bezel over together, esp good if you have those ones with nylon
jaws. Or you could roll it between two swage blocks to shape the
bezel - does both push-overs at once. Make the swage blocks from
hardwood by drilling a hole then sawing the block in half, leaves you
with two pieces of wood each with a groove. Push over enough of the
silver to allow you to still get the stone out, solder on any
attachments, then complete the bezelling.