In the interest of horse-girl infodumping, I recall seeing some at the Gilcrease Museum in Tulsa, OK, and luckily they have some pics for their online collection, thank you Gilcrease.
This one actually has stirrups, looks like the girth attachments are more sophicated than my Dunning-Kruger ass imagined, but the stirrup leathers are, in fact, looped over each of the wooden bars: collections.gilcrease.org/object/84985