Thank you very much for your exhaustive research. I added my comment to the bug report you found.
Well, I did not plan on dedicating my evening to this 
, but I may have figured out the issue. See my comment on the bug report for details, but in short, I can stay with /run/systemd/resolve/stub-resolv.conf, but I had to first put my custom DNS servers in /etc/systemd/resolved.conf. Ugh, systemd has really made a mess of things.
[UPDATE] Please see my final comment in the bug report. I was encouraged by @ricmarques posts here, and by Lukas Märdian's response in the bug report, to put a little more effort into this to see if I could get it working as intended. At long last, I was successful. I'm documenting it in case others find this via search; perhaps I can save others some effort.