If your fridge is similar to mine, the mains heater for the fridge should be on the riser pipe that is also the flue for the gas light, right next to the 12v one.
You can see them in this picture.
When I first got my van, the fridge got warm on 12v, but worked fine on the mains and gas. I pulled it out, and checked everything. both the elements get hot (very hot), but there was a lot of surface rust which made removing the elements from the tubes very hard. I used a mini wire brush in the drill to clean out the tubes, and in the end, after cleaning everything up, and using some heatsink compound to help slide the heaters back into their tubes, I put it all back together. It's worked fine since...
I have a question for you, like you, our barrels only have the small neck, so the pumps that fit through them are not powerful enough to run the shower, and more powerful pumps won't fit in the old barrels... I wanted to fit an inboard pump, but I was not sure how it would prime, if you only have external barrels which are lower than the caravan floor. I had visions of having to find a way of getting water back up to the pump every time you run out of water. So, how do you prime the pump, and how close to the input from the barrels does the pump need to be?