Honestly it sounds like you're on the right track. Freezer powered by inverter, powered by large battery bank, recharged any which way you can.
Use the genny when attended, but throw some solar panels on there too. The "off grid" people do this all the time, they don't even bother using special $2000 hyperinsulated freezer units, the common residential grade freezers are now so efficient that they're within reach of solar+battery.
As far as battery sizing, the amp-hour rating on a lead-acid battery is a lie. If you use it to spec, your battery will last maybe 40-50 discharges before failing utterly. You actually need 4-5 times the amp hour rating you actually intend to use. So if you need 40AH depth of discharge on a daily basis, get a 150-200AH battery. Otherwise you will have very short service life from the battery.
When I hear "40AH", that's a bit smallish so it sounds like an SLA, which are rather expensive per the amp-hour. You'll get more AH for your buck going to a large wet cell battery in the "car battery" form-factor, though you should use a deep cycle or golf cart battery. (i.e. 2 6V golf cart batteries).
Plus, sealed batteries rely on perfect charging. They are not magic batteries impervious to every charging issue; they are only used in applications with excellent charge control (i.e. UPSs). If you are horking together your own charging system, you want a wet cell. If you charge it sloppy, it'll lose some water, and you just pop the caps off, check it periodically and add some distilled water.