Heh, another SuperPonics grower! I bought a 2' x 4' tent with the 12XL. Did one grow in 2017, archived the tent, and then started up again in 2021.
This is the basic setup.
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I've had excellent results with this setup.
Re how to mix the nutes?
One issue is that the EC levels that nutrient manufacturers recommend are extremely high. I use 0.6 EC for seedlings and early very, then jump to 1.2 and finish off at around 1.6. There's no need to be precise (1.2 = 1.3) because the goal of adding fertilizer is to get the chemicals in the res into the sufficiency zone. So to speak, it's an "area target" not a "point target".
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13 gallons? That sounds low by about 5 gallons. When I use the dimensions of that res but use a 9" depth, to account for the height of a net pot, I come up with 18± gallons.
The approach I'd take is to do the math to make about a 400% strength mixture of nutrients. Once you have your nutrients made up, you'll need to empty the res, and then pour in water + nutes until you've hit your desired water level and EC.
The devil is in the details, though. It's OK to pour in 400% nutes as long as you've follow up the nutrient "shot" with the water "chaser" right away but don't delay.
A key point is your source of water.—what is your water source?
Also, how are you planning to empty the res?
My res is rated at 35 gallons, it holds 28, and I replace 26± gallons when I change the res. I use a 32 gallon trash can to mix nutes and a sump pump. My water source is an RO unit fills a 55 gallon cistern. When I do a res change, I pump water into the trash can and mix the nutes, then I pump out the res, and then swap the hoses to pump the nutes from the trash can into the res.
You don't need a 32 gallon trash can but one of those 27 gallon Home Depot containers would make things easier.