Does all that equipment really need to run on 120V?
The #1 waste I see in designing this sort of system is insisting on using inverter to make 120VAC, and then plugging 12 volt DC power supplies into the 120VAC, and the equipment actually runs on 12 volts DC.
The fallacy of that should be obvious. Why not just hot-shot the equipment straight off battery? (perhaps at a different battery voltage).
Because you will have considerable conversion losses both ways, and I see where you are trying to account for that. But what you're overlooking is inverter losses aren't just a percentage, they are also a "flat rate" required to have the inverter "spun up" at all. For low power loads like yours, the parasitic loss of the inverter merely being spun up could be the largest load in the system.
78W is not an accurate number for the switch.
The 78W is a nameplate limit of the PoE switch, you're not allowed to hang more than 78 watts of PoE load on the switch. However the switch's actual draw will be the sum of
- the actual load of the PoE devices which are connected <=78W
- conversion losses for that load
- its parasitic load simply for being powered up and switching
The 78W only accounts for the first line item, but is situational based on your actual loads. Example, suppose you have 5 cameras, that's 35W (well within 78W limit), 40% conversion loss for 14W, and 10W of parasitic "just to be powered up" load. So 59W, that is an example of the switch drawing less than 78W, but it could be more too.
Those other things will need a lot more power
I may in the future add the perimeter lights, and well-pump. Can the inverter be a high 900VA device supplied by low AH batteries E.g. 2 Car batteries rated at 45AH each?
The inverter might suffice but the battery sure won't. It can barely carry the load you are planning. The new loads you want to add are massive by comparison, and will require a much larger battery.
They make DC lights. The well pump might need to be AC but you could give it its own inverter and only turn it on when the pump needs to be running.
But since you do not have the extra loads yet, you'd be spinning up a heavy inverter and eating its larger parasitic ("spun up and ready") load.
Choose appropriate batteries and use within their range.
You see lead-acid batteries with an amp-hour spec, and you think "well, I can use all of that every day for years". Nope. you can use that once.
They don't tell you this, because it's "common knowledge" in the industry. But lead-acid batteries take damage from being discharged. Best practice is to size lead-acid battery banks so they normally do not use more than 25-33% of battery capacity.
But the upside of lead-acid is it's cheap. That's the appeal, of course.
Note that all lead-acids are not built the same. "Car batteries" are built for an enormously large energy impulse (starting an engine) and NOT optimized for deep cycling, and would soon fail even if only 25% of the cycle were used daily. For that, you need a different optimization called a "deep cycle battery". Again only 25-35% though.
Probably the ideal lead-acid deep cycle battery is "golf cart batteries", especially since golf cart owners consider them scrap when they don't make it a full 18 holes once. And so used golf cart batteries are cheap and have a lot of usable life left.
Just the same, lithium and other technologies are not without their limits. For instance some lithium technologies shouldn't be used regularly across more than 80% of their nameplate range without degrading pack life, though the effect is nowhere as severe as lead-acid. (also 80% is certainly more reasonable than 30%).