Well not floating exactly but mostly. This is in an area that has a knee high shelf built into the wall. It sticks out too far to have the desktop all the way against the wall and I will be leaving 10" of usable space between the wall and window. The 2/4s will be mounted by lag bolts into the studs. The pink circles will be pipe legs meant to support the frame. Yellow is the shelf. Orange is 1.5" butcher block that is 72x24. The space is 75" long hence the open area on one end.

How do I mount to the left back corner? Which board should get both studs? Is there too much overhang that is unsupported? I could add more pipe legs if needed but I would like to minimize them as possible. Thanks in advance!

Updated with pics of the space. Please excuse the mess. The pipes will rest on the shelf aside from at least one that will go all the way to the floor. The desktop would be even with the sit/stand desk at the edge of the pictures.

I am wondering if the orientation of the long vs short boards in each "box" is appropriate. Also which wall the long boards should be lagged into.

Complete

Frame

Measurements

Shelf Pic 1

Shelf Pic 2

Shelf Pic 3