Looking for advice

Need to understand better your numbers... Note that Watts (and Watt*Hours) are "complete" units. They "fully" describe the rate of electricity use (Watts, like miles per hour) and amount used (Watt*Hours, like miles driven).

13.5 Amps and 176 Watts...

• Power (Watts) = Voltage (Volts) * Current (Amps)
• Energy (Watt*Hours) = Voltage (Volts) * Current (Amps) * Hours

So, the 13.5 Amps is at what voltage? 12 volts, 110 Volts, or pack voltage (3.7/7.4/etc.)?

For example,

• 176 Watts (rate of energy usage) * 1/2 Hour = 88 Watt*Hours (to charge three packs--All three packs total, or 88 WH per pack?).

Generally, for off grid power, refrigerators are when your system is no longer "small/portable", but getting to be "good sized" and not something you would backpack.

And you have different types of refrigerators. The standard compressor type (something like 1,000 WH per day full size fridge). Or 250 WH per day small/efficient fridge).

And you have propane/120/12 volt absorption type fridge (Ammonia). On propane, they take something like 1 lb of propane per day. On 120 VAC or 12 VDC, they are very inefficient and typically not worth doing on solar.

500-1,000 WH per day solar power system is "small" and enough for lights, a small 12 volt water pump, charging a laptop and cell phone, etc.

3,300 WH per day is enough to run a small/efficient cabin or very efficient home (full size energy star fridge, LED lighting, Laptop, TV, solar friendly well pump, washing machine.

On batteries... A 100 AH * 12 volts = 1,200 Watt*Hour of stored energy. Whether Lead Acid or Li Ion. And roughly, you don't want to discharge your batteries more than ~50% before recharging (and with Lead Acid batteries, you need to recharge them to >~75% state of charge quickly--Or they will sulfate if left to sit for days/weeks/months). Propane refrigerators (may) use a relatively small amount of electricity to run the temperature/flame controller.

The suggested path to follow:

1. Choose your more efficient/low power loads you can (LED lighting, laptop/tablet computers, etc.
2. Typically use Propane (other fuel) for cooking--Although, for small amounts of hot water/etc., possibly solar will be OK
3. Measure your loads using a Watt*Hour meter like the Kill-a-Watt (120 VAC) and/or a DC Amp*Hour/Watt*Hour meter
4. Define when and where you will be using solar (American South West in the summer, Skiing in Canada in the winter)
5. Will you have a tilting solar array? (farther north you go, tilting array can increase your harvest)
6. Will you be parked in shade/valleys/wooded areas? Will you need to have remote panels (100 foot away) in sun while you camp in shade to keep cool?
7. Do a few paper designs of your system (loads->battery bank->Solar Array).
8. Then start looking for hardware (buying hardware without a plan, generally difficult to configure a workable system)

And when you get down towards #7 or so, you may find you have to rethink your system... Too large of loads vs too small of harvest from solar, backup genset (like a Honda eu2000i genset+AC battery charger, etc.).

https://www.amazon.com/s?k=kill-a-watt+meters 120 VAC Energy/Power meters
https://www.amazon.com/s?k=dc+ah+wh+meters DC Energy/Power meters
http://solarelectricityhandbook.com/solar-irradiance.html Solar Harvest calculator (hours of sun per day by location/month/tilt of panels

For the solar harvesting, more or less, >3 hours per day is "solar friendly". Less than ~3 hours per day, solar becomes less able to supply heavier loads.

No problem "running the math" for you--But would really like to understand your loads/seasons of camping/loads a bit better first. Otherwise, things get a bit confusing with me throwing out meanless (to your needs) numbers.

-Bill