Groo the Square tube is double wall or 1/4" and at 3 to 4 ft it should work. I'm a bit confused at the 5000 ft pound comment. (is that what a 1000 pounds piece of equip would equates to?) I get the lifting capacity but by half that seems like a lot.
I'm definitely not a mathematician so you could well be right. If that was the case it seems I might be wasting my time.
what is the horizontal distance from the bucket to the pivot point were the FEL is mounted on the frame?
new lifting strength = old strengthxFEL length/(FEL+boom length)
so if you could lift 1500lbs and the FEL length is 6' and the boom is 4' more, your lifting strength at the boom tip would be 60% of the bucket lift, or 1500x6'/(6'+4') or 900lbs, and don't forget to subtract the boom weight from that number too.
1000lbs with a 5' lever = 5000 ft-lbs
I haven't run the numbers , but my gut reaction is it would take a very high strength steel to take that bending force in a 2" square tube, and the mild steel you'd probably end up with wouldn't stand a ghost of a chance. Putting the tube at the bottom of the bucket an supporting the ends with chain from the top of the bucket could handle it no problem.