Five Year Mystery - Unable to find source of burning smell from HVAC system
Do you maybe have a steam humidifier on the furnace?  If it was wired incorrectly or was damaged it could be trying to heat water when the furnace is not running, or when no water was present in the boiler.

How confident are you on the diagnosis of the electrical issues?  I've heard of underground feeders upstream of the breaker panel becoming damaged and heating the ground.  

Defrost cycle on a freezer.  These will come on every few days, and they often use an electric heating element that may be damaged or running hot because of a bad thermostat.

If this is a new-ish building, do you have a heat recovery ventilator?  These are separate from the furnace, but are generally connected to the furnace ducting, and they will run all year round.  I think I remember seeing a recall for bad HRV fan motors burning up in at least one brand.

Has anyone else also detected the smell?  Noses are all different, and you might be sensitive or mis-sensing a smell.

I would make friends with a home inspector or someone else with a thermal imaging camera and inspect the area carefully.  If it is caused by something getting hot this is one of the best (only?) ways to find it.  Let us know if you solve the mystery.