At first - I'm from Germany and my English/grammar is very bad
and normaly I only read in this forum.
But I realize your problem and I have a few experience in treeless saddles, so I will try to write some words (and I hope you will understand it - if not, asked me again, I will try it again
1. I also think your horse puffing up a bit, I know horses they need up to 10 minutes and more before they relaxed enough to tighten up the girth the right position. In Germany we call that "Gurtzwang" (means in English "girth bondage", I do not know the right word
). Sometimes a girth with elastic part helps a little bit. You can tighten up this girth so that the elastic stretch, if the horse relax only the elastic goes back and the girth becomes not so loose as a girth without elastic.
2. You can also use stirrup leathers with the buckle on top. But most treeless-riders feel uncomfortable, because the buckle press the thigh. But test it! I have also test it and my saddle is not damaged
The problem with stirrups I don't know - perhaps adaption, I ride only with english stirrup leathers all my life. But you can test a special form of stirrups, where the eye for the leather stirrups ist rotated 90° so that you don't habe to turn the stirrup with your Feet in the right position (I don't not know how it is called in English... so look at this picture (it is not a barefoot saddle)
3. The barefoot saddles are complete flexible - the saddle should be flat on the back of your horse when you sit on it. On the other hand they need a few hours of riding before they adapt on the horses back and the riders backside. Without pictures I can't say anything about the fitting.
Best regards (or how do you say it in English ? ),