Consider bumping up the angle size to L3x3x1/4. You should be able to get a 20-0 length for around $40-$50 You dont need tube, plus it's more expensive per lb. than angle. If you have access to a welding machine and some flat bar, weld some flat bar to the ends of the angle and lag it into the wall. One it the front and one in the back should be fine. It needs to be supported on the ends. Or call a small fab shop and have them make them up probably about $100 labor and materials and they probably have the material laying in the scrap. Then just prime them and paint them a nice blue to match your nice cabinets.
We fabricate counter supports for vanities all the time and usually they are made of L3x3x1/4 or 3/8 sometimes TS 3x2x1/4 and the spans are much greater than 5'-6" Sometimes they have a post on each end which bolts to the floor and then they bury behind the drywall, sometimes they just put wood blocking between metal studs that we lag into.