JohnnyGood acquire a kill-a-watt meter. Then measure the device you wish to power.
As a wild guess I'd say the charging times are MUCH too low.
A 100 amp-hour battery is not going to appreciate a 120 amp load from a 1000 watt inverter when it is maxed out.
The power TechOn inverter is pretty much junk.
Bestconverter sells a Xantrex prowatt which may be a similar quality to the Magnum. I'd get the 2000 watt unit.
I hate generators but I think your situation may need one.
The other possibility is to have a rather large solar installation.