Re: Increasing the wattage of the A/C plug to 180w plus?
1) Power supply for Sager says 9 amps at 19v, that would be more like 330w at 12v.
2) One way to reduce the inverter load would be to remove the laptop battery so it is not charging, another is to reduce the screen brightness (in daylight that could be a problem).
Was thinking more of a direct, fused connection from the inverter to be battery so does not use the vehicle wiring. I'd consider just buying a new battery cover, remove the carpet, add an aluminum plate, and mount the inverter on that. Now all you need are a pair of ring terminals to go to the battery and a fused 20A quick connect from a motorcyle starter with a relay to the ignition in one leg.
Disconnect the connector, unplug the charger, and remove the tray and inverter as a unit when need access to the battery.
Run for a while and check for heat transfer to the seat but modern high efficiency switchers do not generate much heat.