Yup your design is the same as picture one. The "Dado Rack"
My question is would this hold up 12 20 Gallon Longs. 240 Gallons 2k lbs.
Easily. It is all wood to wood contact. No real reliance on the fasteners. And the dados can all be cut with a circ saw and a sharp chisel. I gang cut the legs and use a sharp chisel to square the bottom. It's my quiet time. If I am in a hurry I grab the router with a dado cleaning bit. Has a short cutter with a bearing on top to follow the sides of the dado.
I use no glue so I can take them apart later.
I use the dado in all my cabinet construction and have been doing it that way for over 40 years. Doesn't get much stronger than that.
Now on the first rack in the thread I posted you will see the horizontal members are not flush. Since the 2x3 is narrower I didn't want to go as deep as I would for a 2x4. It's still strong. If you are leery use a 2x4 for the legs.
You need to plan a little bit though. Notice how I have a set of legs in the center. That keeps the horizontals from bowing downwards. And it gave me piece of mind for a few dollars.
Since they are narrow stands I did screw them to the wall. Didn't want my then 5 year old to climb it like a ladder.
If you look at Joey's rack it is basically a dado he has created. He just used a ton more wood to get there instead of cutting it out. And in the first picture the 2x under the front horizontals I put so they are in line with the front and rear horizontals. It spreads the front and back but adds no tank holding strength. In theory you could just as well use 1x4.
Now I will say I did add some blocking in between the front and rear horizontals as blocking. And since originally I was putting 8 gallon square angel breeding tanks on that rack I added the blocking where the edge of the tanks were. Not for strength but so if I didn't get the tank on in the right position, or if I was fiddling with it when putting it on the rack it wouldn't fall through.
One caveat to this style of rack. If you don't screw it to the wall you do need to add something to prevent racking of the rack. I am going to let in a 1xsomething into the back wood to prevent racking on racks I won't be screwing to the wall. Same would be true of the sides. I don't use any plywood or foam under the tanks. Look up from the bottom and you will see the bottom of the tank. I did that on purpose so any water that overflowed wouldn't stick around to cause mold. And yes, I have gotten sidetracked too many times while filling. That's why the next step for me is auto fill.