I would say you have a current draw as well. Check your fues box with a test light or a meter. You should not have power your fuses when the key is off. There may be one or two for interior lights and whatnot but only when the door is open. It also could be a faulte door switch or something
Your problem could be a bad battery-- before you chase an unknown-- have the batteries retested. A weak battery will result in two weak battery, as the try to balance the volts between them. Be sure they remove one cable to isolate them as they are wired in parallel to make one large battery.
Also look at the battery connectors. I had the same issue and what my problem was the rubber boots around the connector cables where getting in the way of the connection and pretty much not connecting with the battery fully. I trimmed my rubber boots a little and haven't had a problem ever since.
I would deff check the batteries, make sure they are disconnected because as allready stated if they are connected it won't be an accurate test. just because the batteries are new doesn't mean they r good. I have multiple batteries over my years working at a dealership (Yamaha) be bad rght off the shelf.
As I was typing I just remebered my truck still pretty new I think I was still under 20k had a bad battery replaced under warrenty. but the first start of the day was really slow sometimes it took a couple tries to get it started
Auto Zone and most other stores will do free batter load testing