We currently have a newer (2017) rig with the residential fridge and factory installed 1000w inverter. The inverter runs the fridge just fine, but only the fridge. You can't really plan power usage around the fridge compressor running.
Dual 1000w or adding a 1500w would be good. Otherwise I think having the fridge running and running the coffee pot would be a huge draw. A 2000w may not be enough.
I will echo everyone else with the initial concern, no residential fridge for a dry camping setup. Sounds like you're set on that so, I guess continue with your current plan and get an adequate power setup.
An RV residential fridge typically uses 100 a/hrs per day. Each unit is different but expect 100-120 a/h. The rest of the things in your rig add on to that. Coffee pot uses 15-20a per use. The rest of your usage is pretty incidental. You're looking at a minimum of 150 amps per day if you don't use the furnace. Using the furnace will push you over 200amps.
Four batteries would be the bare minimum just for power storage. That would allow you to discharge to 50% on 1.5 days of use and no solar.
Six would be better. Six batts gets you 2 days of power without recharging. I second the suggestion for building a battery box at the site and put an adequate number of batteries on the ground.
Solar. You use solar already so you understand the challenges at your elevation. I would be bigger than 600 watts.
The residential fridge is nice, but it REALLY SUCKS if you want to dry camp at all. I will not have a resi fridge again.