Head gasket recommendations in Portland, OR area

Tell the shop that you do not feel it appropriate to swap the engine at this time. You just want the head gasket replaced and the OGR manifold cleaned.

 

I would schedule a break from work, to go to Manteca for a week.

[I grew up in Modesto]

 

I'm a little curious about a 'highly rated' repair shop advising you to make a relatively long distance trip out of state with a car that is suffering from a dodgy head gasket - but yea, you need to change repair shops before you swap out the gasket because putting a gently used G4 engine in your G3 seems like adding two rooms onto a termite infested house.
You might want to fix what caused your G3 engine to 'trip it's circuit breaker' first.
Has anyone done a leak-down test to confirm the diagnosis?
Granted.....when an overweight person shows up in an ER panting, clutching their chest in pain, and sweating like a USSS agent at a Trump rally........then you really don't need much in the way of a diagnosis. buuuuuut the folks in a GOOD hospital will usually go through the process anyway......

The engine in your car has 180,000 miles - but everything else in the car does too.
If the car was more properly maintained and your intentions were to drive it for another 180k come what may then I might consider an engine transplant but you probably haven't trashed the bottom end in the engine that you already have- yet.
All of the shaking and shuttering WILL make this happen sooner rather than later but it's a testament to your ownership that you noticed the 'minor' coolant loss.
Many people don't.
They go from "why is my car running rough?" to "%$#@! NOW it's overheating!!"

MY recommendations:
Stop driving the car unless it is to a place that will replace the head gasket - preferably in your zip code.
Have a Oscar-Sierra plan for when your car STOPS 'running rough on the initial start' or at all.
Continue to monitor your coolant - like every time you shut down the engine - but remember that water doesn't compress - and the white smoke that you're seeing isn't the announcement of a new Pope.
It means that you're about to buy another car.

After you replace the gasket, read some of the links at @Mendel Leisk page to fix the thing that probably caused the OEM head gasket to fail in the first place.

Good Luck!