I now have a pasted linen strop, courtesy of @paulFLUS. Thank you Paul!
I have never used one before, so before my shave today I just took a shot in the dark, 5-6 back and forth strokes on the pasted strop, 5-6 on the linen, 10 on the leather.
This was easily my smoothest shave yet. Normally I do my cheeks, then my neck, then the mustache area, then around my chin, usually by the time I get to my chin the blade gets pretty dull and starts to tug badly on my coarse chin hairs, even if the shave started off nice and smooth. This time that barely happened at all, by the time I got to my chin it barely pulled, seemed to cut through without much difficulty.
Each time I pick up my straight razor now it feels less and less like a mystery of "how the f--- do I shave with this sword without decapitating myself" and more like a nice, high-precision manual way of shaving, I'm really enjoying the experience, despite having a neck with all sorts of unfortunate curvature that makes it hard to find good angles.
Hopefully I get my sharpening lessons from the local knife guy soon, I feel like I'm picking up the technique well. I definitely believe -now that I've got a decent technique for stropping- that a lot of my struggle with sharpening was not really in my sharpening technique, but time will tell.