Well I think I've got it now - as of this moment everything seems to be working as needed. Still not 100% certain - but pretty sure. Frankly took so much dickin' around that I hope I have the details straight.
Successful COX to Yahoo email transition with Thunderbird | Cox Community If you run Thunderbird, this post from another user proved invaluable. Note especially the reference to OAuth2 near the bottom - made all the difference. Huge shout out to TCox here.
BlueMail (and presumably other mobile mail apps) - server settings were a given, but continually kept failing at password. Various combinations of old password, new Yahoo password, user names, etc. No joy. Finally stumbled across this at Yahoo
https://help.yahoo.com/kb/new-mail-for-desktop/password-sln15241.html
Followed the link to 3rd party app (still using T-Bird here) and generated a password (16 digit, very random) specific to BlueMail. Plugged it into my test bed device and - got it. Various tests looked good, so fired up a second device, plugged that password into BlueMail and- fail. Huh? Went round and round for a bit with the same results. Finally rolled the dice and deleted the actual account - the account, NOT the app - from BlueMail and started from scratch, blank slate. From this initialized state, BlueMail offered Yahoo as a starting point, so went with that using the recent Yahoo password - that did it. A little more testing and things seemed ok, so I repeated the delete/create on my other devices, all went well.
Like I said, with all the back-and-forth over a day and a half I hope I've got enough of the details straight here, maybe help someone. But really, Cox - this was the best you could do?