when i had my shaker, back then, there was no DPF/DEF. so it would take about 3-4 days before my fridge would shut down. (i never had anything more than water/sodas in it, as i always took my foods out).
with todays trucks, i was told by my current shop, that he DEF tank has a warmer, and that stays on all the time, to keep the fluid warm. that and the fridge are drawing too much current, draining your batteries, to near the level, you need them for starting. since it is warmer now, maybe you can have the DEF warmer disconnected?
and you may also have a parasitic draw as well. you can test that with an amp gauge that has a clamp that goes around the battery cable, OR, you can disconnect the positive battery cable for an inline amp gauge, OR you can insert a voltage meter, and see how much voltage is being drawn, and one by one, remove a fuse to see if the volts drop. that'll most likely be the culprit circuit. for breakers, just shut those off one at a time.
this can take a while...so be prepared to work at it.