"Gee, if I had a 400 lb pro-wrestler son-in-law, just think of how much help he could be with the chores"
A monster cheapo pseudo sine wave inverter would be like the pro wrestler. He'd pick up your refrigerator and empty it onto his plate and after finding out you need a stake bed truck to grocery shop you would rue the day you went the route of overkill.
Inverters have a specification that shows their efficiency at different levels of loading. And I have news for you. An inverter that is loaded to ten percent of it's capacity is like that pro-wrestler.
It would be better to size a RELIABLE BRAND of pure sine wave inverter to take the combined load of both appliances then add 30% for start up of the freezer.
A poor choice can DOUBLE the drain on your batteries.
Example my then $1,800 Trace inverter demands 410 watts max from my battery bank to run an older PC computer the girls use for the x-box.
It was damaging my sense of calm rationality.
I substituted a SAMLEX 300 watt pure sine wave inverter and whoopee, the battery drain is now 88 watts.
How much energy ($$$$$$$$) this has saved in five years, scares me.