First off since the batteries keep draining down I would have them load tested, most auto parts stores will do this for free, I know you said the batteries are new but I have seen new batteries with shorted cells.
IF the batteries are good it sounds like you have a draw and if that is the case you have some options. But first check your fridge for a high humidity switch inside the door, I have seen this happen before when the starting battery is wired to the fridge and that switch is ON it will draw from the battery even though the fridge is OFF, that might be a long shot but something that should not get over-looked.
One solution for you is to add a manual battery dis-connect at the battery, easy to install and it will prevent the batteries from draining down on you.
The other option which can be time consuming is finding the draw. Get a good 12 volt test light and disconnect the main ground from the battery, hook one end of the test light to the cable you remove and the other end to the neg. battery post, the light should be faint, if it is bright you have a draw. Go to the chassis fuse panel and start pulling fuses one at a time until the test light goes faint then you know which circuit is causing the issue. Also on the battery look at any smaller wires that are wired direct to the battery they can be suspect as well. Once you find the circuit you can start looking at components in that circuit.
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