So I ordered an additional battery, as well as a new pump and an inverter.
Now using two 12v 100Ah batteries as my battery bank, wired up in parallel to double the amps, or 1920 watt hours of power factoring 80% DoD. The new pump draws 57W, which should give 33 hours of pump runtime without any sunlight charging the batteries. I'm sure there is also some draw from the inverter as well, but I don't know how to calculate that, but as long as I'm over 24 hours I am happy. I just got up to check it and the battery bank is 12.5V or 80% (it's 5AM atm).
My system now looks like this, sorry for the mspaint. I'll still keep the DC fuse box in the event I want to add any DC components, maybe a light out in the shed. My main concern currently is that I don't have a breaker or a fuse between the inverter and the battery, however my only intended application is the low wattage pump so I'm not too too concerned for the time being. Plus the inverter has under/over charge, short circuit protection and a built in GFCI.
The inverter I bought is the Renogy 1000W:
https://www.amazon.com/Renogy-Inverter-Battery-Converter-Saving/dp/B07JMQ27WJ/ref=sr_1_5?keywords=pure+sine+wave+inverter&qid=1650784556&sr=8-5&th=1&fbclid=IwAR1VxOyaYs_Y25MsPHj8XsHuYUTqR5BJ065nupeU0C7CEwcef0C3BgAo2nE
The inverter is rated quite a bit more than my intended application, but it was on sale for 20$ more than the 700W model, and it lets me future proof.
The pump is the Laguna Max-Flo 960:
https://www.amazon.com/Laguna-Max-Flo-Waterfall-Filter-1920-Gallon/dp/B0079WZGWE/ref=sr_1_1?crid=1N7NF2XWOJEVF&keywords=Laguna+Max-Flo+960&qid=1650807559&sprefix=laguna+max-flo+960,aps,323&sr=8-1&th=1&fbclid=IwAR2ediD99suNwUcp16HfvHhhUFRHySRKaXM7kk5v_-Awtfvqv0bE4h2VLiQ
They key selling points for the pump to me was that it's designed to run 24/7, handle suspended solids, and low wattage. I wish I could have found something similar but as DC instead of AC. Oh well, that's what Inverters are for.
GPH: The output from my bog filter filled a 5 gallon bucket in 45 seconds, which should mean that my bog is turning over 400GPH, which is slightly more than what I wanted, making it ideal I think.
My current formula for circulation is:
I wanted a bog that was 20% the volume of the pond (300 Gallon pond, I'm using a 55 Gallon barrel as the bog filter, which is under my mark but I also have a settler tank and an additional bucket filter before the bog)
The GPH I was aiming for was 330GPH (bog volume * 6) this turns over the pond at least once an hour, and keeps the water moving through the bog nice and slow. The video I watched for this information is from Ozpond,
Hopefully this all works out, I think the only issue I might have is requiring additional filtering, which can easily be fixed by picking up another 55 gallon barrel and setting up another bog filter or maybe even some K1 media. But I also intend to add some plants into the circulation system before that though. I definitely do not expect "crystal clear" water but just safe, moderately clean, algae free water.