Sorry to be obnoxious about it, but do you have reason to think this will give me something, like the ability to use a fully SSL or TLS encrypted connection?

Modest does work atm, and since my mail provider clearly states that it does not allow unencrypted connections, I have to assume that STARTTLS works (initially unencrypted contact to kick off an encrypted connection).

But fully encrypted would be safer.

On a side note, would upgrading these packages also somehow improve the browser?

The debugging unfortunately did not help much; the dbus method gives very little information.
Same for the command line method (with MODEST_DEBUG=debug-code:log-actions:debug-objects:debug-signals).
None of it pertaining to connection protocols and such.
I could show you, but it would be pointless.
Back to non-descript error messages and trial & error.