Have you considered paralleling three units of 4 or 5 kilowatt inverters?
That will give you all the power you need.
Also since you are talking off grid you will have batteries. If the day is a bit cloudy and you need more power than the panels can supply, the batteries will take up the slack so to speak.
You might also spend some time to make up a chart of power consumption against clock time then develop a few house rules about what is allowed to run and when.
Grid power is a relatively bottomless pit in terms of power availability but solar power needs to have it's limitations fully understood and maybe worked around.