That's a clever idea I hadn't considered!
FWIW, I did some research on ways around the new Microsoft authentication garbage. There are a handful of mods that replace or augment auth in various ways, but none of them are particularly great. At this point I'm mostly looking into this as an academic exercise and because I suspect that Microsoft will eventually cut access for at least one of us "accidentally" at some point.
Some things I've been reading about…
https://minecraft.fandom.com/wiki/Yggdrasil
https://wiki.vg/Authentication
https://wiki.vg/Microsoft_Authentication_Scheme
https://wiki.vg/Protocol_Encryption#Authentication