And a whole different route; does your amp have a direct out on it?
In other words a line level signal that could be sent directly to the interface.

That might eliminate the need for a mic in the first place.
I prefer recording guitar/bass this way sometimes, unless the sound of the amp's speaker is absolutely necessary.
Even then it can sometimes be emulated.
Just another route to consider.

One other thing to try is putting the mic *right in front of the amp facing the amp (with the monitors well behind the mic).
Put an SM-57 right in front of the cone (a little off center of course) and about 8" away from the speakers and any background monitor issue may become much more manageable.
In other words your second solution, monitors behind the mic and a ways away, and with the mic right up to the amp speaker.

Watch your volume levels so as to not damage anything, but this method can be used successfully if done carefully.

I do not work here, but the benefits are still awesome
Make your sound your own!