Quick update,
The error has continued, but I have tried a few things and found a fairly robust, if not tedious, fix.
I found option 3 in the original post to work best
Steps
1) press the "xbox" button, and return to your xbox's home screen
2) hover over BF1 and press the "menu" button (right above the right stick) and select "Quit" at the bottom of the pop-up menu.
(This will stop/close the BF1 game rather than 'minimize' it.)
3) reopen the game and log in. Try to join a match, if the error occurs again (Error Code: -34601), return to step 1 and try again.
Sometimes I have to iterate a couple times before the error clears up, but so far this method has worked three times in a row; without resetting or powering down any equipment.
If anyone has any other ideas, or knows the root cause, feel free to let me know. Maybe I just got lucky three times in a row.
