OP here! My doctor called in a 1x a week rX. I asked to be lowered down to .0375, and the pharmacy had one box. (I've been adjusting my dose down... long story and not really related to this post.)
So I was using the cut patches for one week-- that is, one .1 patch, cut in two, and I used one half in the first part of the week, and the second half after that. I felt the same. But it was only for one week. YMMV.
I am glad so many women are getting treatment, but this shortage is really, really ridiculous. I feel like we are still in the Dark Ages of menopause treatment, and this is one aspect of that.