1. The "Batterystuff" calculator is assuming 100 percent efficiency. No such inverter. Most will run at 70-80%. That's OK. A 400 watt continuous rated inverter will usually give you 700 or more "Startup" watts.
Example at Amazon:
BESTEK 400W Power Inverter DC 12V to AC 110V Car Adapter with 5A 4 USB Charging Ports
Above is not a link, but a description. Cut and paste it in the Amazon search box.
2. If your tow vehicle is rated to supply 20 amps DC to your trailer connector charging line, you should be OK.
BUT............... Remember that your trailer brakes pull power from the trailer battery when they are applied, so the charging line has to provide power to them also. Also, if your trailer battery is not fully charged at the start of the trip, the charging line may be overloaded with the refer running. You should be fine on this as long as the trailer AC shore power is connected for 12 hours or more before you go on the road.
2015 T12RBST Flagstaff Hardside
2008 Itasca Meridian 37H