If you already have the fridge and dual battery I'd recommend going the solar route. Less weight and less fuel needed, probably cheaper in the end too.
Grab a DC-DC charger with a direct solar input if you don't have one already, the Projecta IDC25 is a popular one that's lighter on the wallet, it can charge the secondary battery from both the alternator and the panel depending on whats available. You can easily wire the solar input to a Anderson plug, then you can shop around for a solar panel that fits your needs, flexible, folding, permanent mount, etc.
I use this setup to keep my secondary battery and detector battery charged along with keeping the fridge cold.
You can also use a basic solar regulator instead of the DC-DC charger which is cheaper but they won't preform the fancy charging cycles to keep your battery topped up and in best health.
The GPX batteries are easy with their 12v chargers and I'm sure there are 12v or USB powered chargers for standard battery sizes out there.