Okay. As a [temporary?] workaround, I disabled all plugins at once by moving them into another folder. Suddenly, I'm now able to login to the Admin UI, and successfully change my password therein.
This looks like it might be due to one of my many plugins. It'd be a long process to see which one(s) conflict with changing a password in the Admin UI, so I'll search around to see if known problems have already been reported — before testing one at at time.
Fwiw, here is my plugin list; yep, some of them have been orphaned. Unable to grab version numbers at present since they're disabled from the UI, although I keep the latest versions of them, where actively developed. Also unable to remember which ones were active for the same reason (most are, a few are disabled) — although I can look at one of my live sites (similar installations) and take a guess (denoted with [d]).
[d] AF Extended Live Archives
Comment Email Responder
Custom Query String
[d] Filosofo Comments Preview
Google XML Sitemaps
Link Library Listed
No Self Pings
Spam Karma 2
[d] WP db Backup
Yet Another Related Posts Plugin
Of anyone knows of plugins that'd cause password changes to result in 403 and prevent Admin UI access, it'd be great to know. Also wonder if it might be due to a combination of plugin with localhost installation — but if the latter isn't relevant, is there a way to move this thread to the Plugins and Hacks forum?