The helmets on those Georgians do indeed very closely resemble those worn by Polish pancerni.
As to Turcomen, the best option is probably converting Siberia Miniatures Basmachi; at least they're mostly depicted in the correct clothing You'd 'just' need to back-date the firearms somehow and swap the heads for ones wearing huge, rounded, shaggy hats. An easier, if less accurate, option might be to start with the Copplestone Back of Beyond Caucasian Cossacks and achieve most of the effect with appropriate painting.