"SWAG" means Wild ____ Guess.
Try the other mechanic. First of all, someone should chack for stored codes even if the light isn;t on.
Fuel pressure is easy to check by any shop. It's basically just measuring the fuel pressure in the line when the engine is on.
Additionally, someone may want to hook up an analyzer and check those things associated with the spark pulse. Yes, the CPS signal can be checked that way.
thee possibilities come to my mind:
1) the fuel pump is failing and is unable to maintain proper line pressure.
2) the Evaporative Emissions System has a problem, perhaps a saturrated charcoal canister, that is not allowing the gas takn to readily draw in air to replace the gas getting pumped out. That would allow a vacuum to form in the airspace in the tank, preventing the pump from pumping enough fuel to keep the line pressurized....which could also weaken the pump.
3) something is getting heat sensitive. The CPS is a poassibility. If this has a coil pack, that's another possibility.
It's also possible that you simply have a bad sensor. Perhaps the temp sensor is bad, telling the ECU that the engine is still cold. That would cause the engine to try to run too rich to start.
Perhaps the MAF sensor is bad.
Any garage should be able to troubleshoot this.