Thanks again. I'll pull the processor board and have a look at the power supply and replace any diodes marked ZM or ZS.
I'll definitely replace the battery, I think Digikey has the correct one. I'll leave the electrolytics as-is unless I see anything that looks suspect.
Had the scope off all night and cold started it in the morning without issues. I'll do this over the next fews days for good measure but thing are looking good at this point.