Norcold Compressor Refrigerator
The 12.3 you mention is before there is a load. My 12 volt outlets typically read around 13.0 on a charged lifeline AGM battery bank after sitting for 4 hours. Your voltage is probably dropping further under load. That sounds lower than I would expect to start. Have you measured the voltage also at the battery? 12 volt fridges have quite a bit of amperage draw. In my prior RV with a 3 way dometic fridge, 12 volt was not recommended except for when the engine was running due to dramatic battery drain. It simply switched automatically to propane when I turned the engine off and 110v if I plugged into shore power.
I realize your fridge isn't an absorption style like I mention above but it does pull 3 amps and it needs likely more to start the compressor. If your voltage at the deep cycle battery is also at 12.3 when parked for several hours, it is suspect. The voltage should be much higher. 12.3 indicates a 65% charge. You should always strive to keep it above 12.2 for longevity. (12.2 is 50% charge)
Aside: I know some say that lifeline AGM batteries are too expensive as compared to traditional flooded cells but I have been very happy with them and like the virtual elimination of corrosion, 1% voltage drop per month when parked unplugged verses 10%, and so forth. I've even changed the starting battery in my Subaru Outback to an Exide AGM. I intend to do the same with my motorhome starting battery when it comes time to replace it.
History: '08 View, '05 Chinook, '01 Jamboree 24D, '78 Apache Popup, 81 Komfort Tlr,
84 Mazda B2000 'w canopy,
Tent from wedding shower in '96