I am currently camping in Oregon up from the good old Inland Empire in my 2017 Greyhawk. Strange coincidence.
1. Set the fridge on AUTO and it will select either 120 or propane as needed. At home make sure the rig is mostly level for the fridge to work. If it is hot there it will take overnight to cool. Load the fridge with items that are already cold or it will take forever to chill things. You can use a standard good quality extension cord at home as long as you don't run the air conditioner. It will power the fridge just fine. If you need the ac to cool the insides down for loading, fire up the generator and use both units then turn it off when done.
When you are driving the fridge will automatically run off propane. As it has electronic ignition it will relight if the flame goes out. I don't seem to have any blow out problems in my Greyhawk as I never get an error message saying there is a flame problem. It typically can give you that error if it fails to light in the beginning after refilling until propane can get to the fridge.
The propane will last many days unless you run the furnace or do a heck of a lot of cooking. I wouldn't even blink at running the fridge for a week on propane.
The only reason to run the generator while driving is to run the air conditioner. It would be extremely wasteful to use the generator for the fridge. With the testing I have done my fridge seems to cool a bit better off propane.
I have the same fridge and recommend starting it as soon as you can get the rig level and plugged in. If you can't plug in right away go ahead and use the propane at home.
If you will have people riding in back during the drive you may want them to be comfortable so fire up the generator and run BOTH airs. If it is only 2 people up front your regular ac will be just fine but it won't do anything for the people in back. It all depends on how much you like the people in back.
As far as how to run the airs for max cooling I have real first hand experience here with my 32 foot Greyhawk. On hot days you will need BOTH units running. The main area unit should have the downward vents OPEN so it forces air straight down. You get more airflow to the main area that way. But it is not enough. On the bedroom AC, close off the down vents so the airflow feeds the air ducts as some of these feed the main area. Your bedroom AC will add cooling to the front area and is definitely needed. Also, the bedroom will get very cool and the AC will cycle off. I recommend setting its thermostat a few degrees lower than the main area's AC so it stays on longer. Of course if anyone is laying on the bed they may get cold.
With the generator running you will have 120 volts to all outlets. You can use items that don't draw a lot of power while both airs are running. Fans, laptops, etc. are all fine. No hair dryer though. If you have the power management center you can use the microwave as it will turn off the rear compressor temporarily while the microwave is running so the 30 amp power max is not exceeded.
If you run the generator for extended periods of time, allow it to cool down before turning off. Shut down the airs and let the generator run for 10 minutes or so with no load.
I dry camp a lot and always travel with a full tank of water. If you will be at a hookup site just fill the tank to half or less to save the weight. Not sure if it will make a big difference in mileage or not. Probably not enough to jump up and down about.
I just installed an engine monitor so I can watch my mileage. I basically like gauges and gadgets. On my trip to Bend, Oregon I averaged 7.5 mpg until I cleared the Mt Shasta area. Mileage started out at above 8 but the Grapevine and these other mountain roads dropped it. Once I cleared Mt Shasta and hit mostly level roads I was showing 9.2 mpg which surprised me as this shoe box is not designed for efficiency. My best mileage on the second leg was driving at about 63 mph as I was following someone towing. This helped raise my reading. My first leg was at 70-75 with wind.
Your drive will be a LONG one and very tiring for the driver. If you have multiple drivers it won't be so bad. For me, my wife volunteered me to do it all as she is a wimp when it comes to driving a big vehicle. We stayed at a couple of campgrounds on the trip up which helped tremendously. Also stopped for gas at about 1/2 tank every time mainly to stretch our legs. I still hated the long drive.
Enjoy your trip! The scenery in Oregon was way better than the 5 freeway in CA.