The 22w with inverter drawing 2.5 amps is at half the 20hr rate of a 100AH battery, so you get longer time than just using down to 50% (50AH) due to Peukert.
You get "inverter amps creep" upwards as battery voltage falls when the inverter tries to maintain the watts, so that 2.5 amps could end up as 3 amps after a while. This will reduce the Peukert difference from the 20 hour rate as time goes on. Still more time though.
The big inverter vs small inverter for small loads was gospel, but when I measured for that in some tests I posted about a few years ago, it turned out not to matter. It was because the small inverter was on thinner wires to the battery than the big inverter, so it was a wash. Especially if the small inverter is plugged into the Winegard 12v socket.
Also you can't compare inverters in inverter/chargers with ordinary inverters. Those inverter/ chargers have big draws to run their fancy features just on standby, that ordinary inverters do not have.