[bassman]

Yes the joist run the length of the tank.

The reason I cut into the wall is to put some of the load in the exact same spot as the load from the wall. Which happens to be a 6" wide load bearing wall in the basement. One joist sits right on the wall, the next on is only 5" from that one, into the room.
That is why I have another 4x4 inches away from the one in the wall. From there it goes to industry standard, 16" centers. So 9 of my legs will rest directly on joist. The other 3, in the wall, sit right on the bearing wall. So in total I have 12 points, 250 lbs per point, 750 per joist. Which I have minimized even more by placing the legs that rest on the hardwood on 2x4 runners, this will distribute some of the load vertically across the joists as well.

My joist only run 11' between bearing walls and they are 20" tall, very strong.

I have shown my plans to a couple engineers I used to work with and they all agree, I am WAY over building this stand and the load is nothing to be concerned about. Better safe than sorry.