Burned out Clutch :(
Turns out, there is supposed to be some play in the clutch lever. Since my clutch lever was too tight, I have apparently been riding with my clutch partially engaged for a few thousand miles. After an hour of ridiculous stop and go traffic, my Speedmaster decided it had enough, and the gear no longer engages. Yet another expensive lesson in motorcycle maintenance.
I'm glad I'm learning these things on my Speedmaster so once I get a Thunderbird I'll be ready!