Watts are watts, some math conversions will give you an idea how much you are really putting out & can use.
Powerfactor (efficiency) is the loss you'll have to account for & the full load capacity of the gen will be the other issue.

Generator:
1100w = 120volts X 9.16amps, (8amp rated = 960watts?)
80% load = 880watts
92% load = 1012watts

Charger + PS:
Protech chargers are 200w per channel max, (800w max total load) +10% for loss?
880w + Powersupply inefficiency = 15%? (more like 20%)
PS draw = 1012watts?

If you don't need max charging ability you'll be safe.
Limit your self to 9-10amps on the 4s packs, & 18-20amps on the 2s packs.
(all four channels charging)
Less will be better for your generator.

If voltage falls off or the PS has an issue with the gen output from sinewave clipping you'll have to lower your amperages.
If the generator boggs or trips a push button breaker, lower your amperages...