I agree,
F
FJB
, that doing a nice straight level stand is the most elegant solution. For me, that elegance goes right out the window when some of the legs require a quarter-inch or more of shimming. I do what the OP is planning, i.e. built the stand to be a permanent, non-moveable fixture for that precise spot on the floor and no other.
Attach a length of 2x4 to the wall at more-or-less the correct height...get it level by eye...and then attach to it the length of 2x4 which will be the back top of the stand, carefully and perfectly leveled and at the exact height desired. Build the rest of the top frame attached to that, and temporarily supported perfectly level using Workmate portable benches, chairs, whatever. Then measure and cut each individual leg to reach from the top of that upper frame all the way to the floor. If the floor is really wonky, I will cut the ends of these uprights at a slight angle to match. Then build the bottom frame, which sits right on the floor and is not level, but which ties together the top and bottom frames. Make certain that all the uprights are perfectly plumb and that the upper frame remains perfectly level; they sit inside the corners of the top and bottom frame. Now it's child's play to measure and cut all the individual verticals that sit on top of the bottom frame and extend up to the bottom of the top frame, and carefully laminate them to the existing uprights. I usually have two of these laminated to each upright, creating columns consisting of 3 pieces of 2x4 apiece.
This thing becomes part of the house; it ain't going nowhere.