Yes to Callirhoe. Your two best options seem to be C. pedata, (perennial with a swollen root), and C. leiocarpa (taprooted annual).

Hmm, well and there may also actually be 2 different varieties here?

Because some of these appear to have wiry, green stems with very thin "cannabis" leaflets...and the other has thicker, reddish stems with grassy leaves?

Just from the name alone, I would guess this first type might be Callirhoe pedata (Palmleaf Poppymallow) - as it does have "palm leaves" and also blooms ranging in color from white to pink to purple. But, these thin, palmate leaves don't actually match the more lobed ones shown on the dried specimens?

And I'm still not sure what this second type might be - as Callirhoe leiocarpa (Tall Poppymallow) also has more Geranium-like leaves.

So...I'm still confused! They don't quite seem to be Callirhoe pedata (Palmleaf Poppymallow), Callirhoe leiocarpa (Tall Poppymallow), or Callirhoe scabriuscula (Texas Poppymallow)? If not then, what else could they be?

Hmm, well some Mallows planted at a local wildflower garden were labelled as Callirhoe involucrata (Wine Cup/Purple Poppy Mallow). They were more pinkish than purple, though. Nonetheless, I'd still say there's a good chance that they purposely planted the local variety there and properly ID'd it. Not necessarily...but with a decent likelihood?