Appreciate the responses and apologies for the delayed response. Just returned from a week of beach camping with the family. Had vacation scheduled so I charged the batteries and went last weekend. I will certainly check out my small solar panel. A few findings over the week:
My coach and house batteries charge when connected to shore power. They consistently read over 13V this week while camping with 50A service.
Today after being in storage for 1 day, both house and chassis batteries read 12.3V.
When checking the batteries in storage, I noticed that the microwave clock was ON even though I had certainly turned the inverter switch off. I went outside to the inverter and hit the inverter toggle on the top left and the microwave went off. I will return to check the batteries tomorrow after work as well. Perhaps the inverter switch is not working. I did hit the toggle on the inverter last weekend when first troubleshooting so perhaps that 'disconnected it' from the inside switch.
The inverter being on or turning itself on explains the house batteries dropping. I was/am still concerned with how new chassis batteries could drain. However, while camping this week, I noticed that a 'Cargo Dome Light' wheel switch was rolled all the way up. I have no idea where these lights even are (presumably in the cargo bays) but since the switch is on the dash, it is likely on the chassis batteries. I have never touched it so I can only imagine that my 3 year old son found it was fun to play with. I am hoping this explains the chassis batteries but I will be checking them daily for the next week.