Too much too soon can also
Too much too soon can also apply to all the various forms of exercise for the feet as well. I never really do those exercises as I tend to think the best way to adapt to barefoot running is to run barefoot and cease wearing support foot wear. On really, really bad days when my form wasn't so good and my left 2nd metahead is tender, I"ll wear my zero drop keens which are more flexible than normal shoes with a wide toe box and zero support. They have just enough protection that I relax into them and allow the foot to heal faster.
From what I've read about most other BF runners; the "norm" is hard to pin down. Without fail, everyone has to slow down in speed and distance for weeks until the soft tissue and bones adapt enough to form a weekly BFR routine. Some do the various strength training and others just run barefoot and ditch the supportive foot wear. A small percentage of the folks have similar issues to what you and I are experiencing with the good news being that it will eventually stabilize to the degree where you should not notice it.
In all cases of folks that stuck with BFR for a year or so, things do work themselves out regardless. If I were you, I would focus more on proper form and getting naked feet to concrete to get that skin adaptation going.
Three things that helped me a lot:
1.) stretch, stretch, stretch (CAREFULLY and less so on your running days!). If you can't touch your toes, start working on that. I can give you some details if you want but the most important thing is to not allow those muscles to stay chronically short. To that:
2.) Trigger points and mayo fascial massage. Some of your soft tissue issues may be caused by chronic muscle tension/shortening at various points in your legs. I spent a few hundred dollars on medical texts and toys on the matter and it helps quite a bit.
3.) Don't go crazy with all those foot exercises; it's more important to learn the "place foot lightly" form and learn to stay relaxed while running.
TIP: If you find that "babying" a chronic issue isn't helping, stop babying it and use it more so long as the pain doesn't prevent it and there is no major damage to the connective tissue and the bone structure. I've found that a little push beyond a perceived limit does wonders but it needs to be done with discernment and caution. Most importantly, don't get angry or frustrated. The body doesn't do so well with that
Good luck. Your journey is likely to be more difficult than most, mine was and still is due to connective tissue issues, but with time and an open mind, you'll adapt and find yourself running a weekly routine without shoes.