Test the ecu coolant temp sensor, on the tstat neck pointing forward, with two spade contacts in a tee shape. It's a thermistor, and you need an ohmeter and thermometer to check it. Specs are in the fsm. Resistance varies with temperature. If it fails, one failure mode adds cold start enrichment all the time, any you are running too rich to fire the charge after the engine warms up all the way (i.e., will run longer in cooler ambient temps).

How is it to restart after a stoppage event? Have to cool down for a while or will restart immediately, or what?

After a stoppage, does it have spark? When cranking for a restart, how does the exhaust smell?