LOL. Admitting you are an engineer is the first step towards getting help... That degree means nothing to me, but let's try to help each other nevertheless.
Your big miss mr engineer is that the compressor fridge does not run all the time. That is my pet peeve for people answering forum post who do not have experience with the subject. No offense, but people who own compressor fridges know they do not run 100% duty cycles. You know what you know, but not what you need to know. Now you know more.
I can't tell the OP what % his fridge runs. I just guessed 20% as a round number. This means 12 minutes of every hour. So every 5 hours you get a full 60 minutes of run time. Probably that big front door fridge runs more.
As you know in reality, the solar panels work in morning and evening light. My panels will have the system charged back sometimes before I get up, before your 4 hour imaginary window. Panels do not need to be at 100% efficiency to do work. They are always at 18 volts but the amps vary with light.
My fridge starts up with 4 amps and runs on 3 amps, the battery will be back to full voltage, even with the fridge still on, in the morning off of only 200 watts, before the magic hour, in the forest woods. I also run lights and fans and charge devices etc.
The panels will have extra capacity available during a normal sunny day, so the battery will not be drained in the daytime. Batts will charge and run the electric items at the same time. I always try to charge my devices early in the day when the sun can charge it so I start the evening with full battery and no drain from chargers.
Doing math is good but you have to consider all variables. Leaving some out ruins it all. Thinking an 8 amp fridge will pull 192 amp hours (2304 watt hrs I guess) in one day is a big doodo.
For the 20% duty cycle possibility then 460 watt hours if I did that right. I use amp hrs not watts. You used 4 amps in your math, so thats just half, so 230 watt hours not the 1152 you came up with. The fridges must run more than 20% of the time because these are small numbers, but they do not run all the time.
So, there ya go. Hope this helps.
So for a big 8 amp electric fridge it is a harder decision to make than for a 3 amp fridge because you will need a bigger battery bank than most RVers have to cover for cloudy/rainy days.
My experience is that it is worth getting more battery to have the electric fridge. They do not need to be level and can run 30 Degrees off level and be fine, vs the 3 degrees the propane ones tolerate.
I would get an electric induction cooktop if I were to do it over, and just keep a camping stove for backup.
Batteries can last 6-10 years. If say 7 years then a $600 set of batteries cost $85 per year. Propane is $17-22 or so per tank. You have to have batteries anyway, so lets say normal would be a $300 set of batteries, but you did a $600 set for the electric needs, so thats an extra $43 per year or two tanks of propane. You still need propane, but a full time boondocker will need 1 tank just to run a fridge per month times 12 = 500/year. yikes. Even if my math is off a little bit these are big numbers.
