Well, turns out the oil is A problem, but not THE problem. Put a quart in and the cluster died again after a couple minutes and the bike stalled just as I made it to a parking lot. So it must be electrical after all. I pulled the battery and walked it back to the house and put it on the charger. Showed 22%. It was fully charged prior to taking it out.
I'm leaning towards the battery/charging system being the culprit, but I'm not confident in that assessment. The charging Mod failed months ago, but I never experienced this issue until now. So why now?
Could there be a correlation between the oil leaking and the electronics? Maybe. Won't know until I get it apart and check the loom. Is the failing cluster a symptom of the stalling or is it due to the engine being starved of oil? I don't know that yet either. The quart I added didn't even register in the site glass, which means that engine was bone dry. For how long I don't know. I do know that I never would have discovered the leak without the electronic failure and stalling, so if the two are not related then the one problem may have saved my engine. If it's not already damaged that is.
Just waiting for the battery to charge and then I'll walk it back to the bike and see if it makes it home.
NOTE: I also placed a VOM on the battery last night after disconnecting the charger, and the voltage steadily dropped one volt per second. Not sure what it means yet, but it's interesting.