I think what he's saying is the 24 volt panels with MPPT controller essentially start up more quickly than 12 volt panels-because they have more voltage headroom. I have 12 volt panels and a friend has the aforementioned 24 volt household panels. His do start up faster in marginal conditions and give better output in low light. Nevertheless all are severely degraded by shade. Where I see hope for you is that it doesn't appear that you always camp in full shade. It appears you will see breaks of sunlight which will hit with full charge-even briefly. Some of your sites appear to have very little or no shade. Perhaps you can slightly adapt your choice of sites with solar as consideration. Beautiful pics btw. Even in shade I get a couple of amps with my system.
Here's a thought: A 24 volt 250 watt panel (less than $200) such as Shadow mentioned on a hinge on back of trailer. Hung high with awning like support-swing it out when camped. With MPPT controller I'm sure you'll see 15 amps in the sun at times. A few amps in the shade. It sounds like you're (like I am) very frugal with your power. Even a 20-30 amp hour infusion in sub optimal conditions is very significant and beneficial.