For my next bike, I either want a touring frame or a mixte, but since my Surly CX is already a jack-of-all-trades commuter/tourer/just fun to ride bike (if a little heavy with front and rear Nice Racks), I'm leaning towards a steel mixte frame.
I haven't seen many of these, so right now it's basically looking like the Soma Buena Vista frame. I'd like it with Nitto Moustache handlebars, bar end shifters, and a set of fenders, maybe a lighter rear rack. Any suggestions aside from Soma?

I have a vintage, Austro-Daimler Mixte. That Soma is one beautiful frame. I don't see how you could go wrong with that one.

The type that uses a single larger tube, with shorter stays from seat tube
to rear dropout will be solid riding.

I built up a light 531 Mercian Mixte, [for a friend] front end
was positively noodly.

the cheaper one used thicker walled tubing for those mixte long tubes
it actually was better.. in not being able to pull the wheel sideways
with the handlebars.

A mixte is a pretty solid frame design. If steering flexed the frame to the point of pulling the wheel, I would be looking for a crack in the frame or a weld.