HvBuzz- keeping a fridge running and cold on battery power is a tricky thing. I can't help with details there without a lot more details, BUT I will say you are right in your thinking about getting it to temp and loaded before you go off electric!
A couple things to help you along in your quest to keep things cold 1. A full fridge will stay cooler than an empty fridge as does a closed fridge. 2. Set fridge to coldest temp before switching to batteries, don't forget to set to higher temp (but under 40*F) when you switch over to batteries - less cycling=less battery usage.
Bring a cooler for frequently used items, and items that don't have to be chilled below 40*F - beverages, mustard, pickles, ketchup etc.
If you anticipate opening up something that will need refrigeration during your trip (new jar of mayo etc) - chill it at home and store it in your beverage cooler. Less battery juice to bring it down to temp, plus it will help keep drinks cold.
Put a few gallons of frozen drinking water on the top-shelf of your fridge when you go on battery power, your fridge will cycle less. Consider a cardboard 'berm' for the bottom half of your fridge. It will help to keep cold air in the fridge.
Think of the cold air like water, when you open the door on a front load fridge, the water pours out from around everything in the fridge. A snug cardboard 'dam' for that cold air will help keep at least some of the already cold air in the fridge. (This isn't a great idea if you have a lot of door storage btw).I use this method off-grid and when power goes out. Things that need to be the coldest go on the bottom, and those that will be reached for most infrequently go behind the 'dam'. Things used most frequently and the fastest to be used up, go on the top shelf.
Freezing as much as possible before a trip is also helpful. I once made a freezer cooler. I duct-taped it shut so no-one could open it. Things were still frozen 5 days later. I pre-prepped food and froze everything flat (laying on a cookie sheet) in gallon or quart freezer bags. They pack tightly together standing up in a cooler that way. More ice in ziplocks to fill dead air and ta-da. These frozen bags of food also serve double duty as ice blocks when you put them in your other cooler/fridge to defrost before you cook them.
Those frozen drinking water jugs? Rotate extras in your freezer compartment when you're not on batteries. Be careful you don't bust the jugs- remember, water/ice expands as it freezes. Do not overfill jugs, and tip narrow-necked jugs to get as much surface area as possible to avoid container failure.