Hi, Andrew. I would be much happier with a brace or bracket from the outside of the countertop at an angle into a stud every 32" or so. That is just a much stronger structure and should not interfere too much with your knees. A 45 degree angle brace would be ideal. In my opinion, 90 degree metal brackets are not worth the effort and will bend pretty easily. How you attach them to the counter top depends on what material you choose for it. Maple 2x4s or similar could be predrilled and screws run right into the bottom of butcherblock. You would want to run a hardwood doubler on the outside edge of a laminate-topped countertop. I do think that a solid wood 3/4" top would give you problems.
Are you going to install headers and footers in the opening? You should and they should be made of 2 pieces of 2x4 nailed together with a 1/2" piece of plywood or chipboard between them for dimension. The top one should rest on a queen stud and they should both be toe nailed into the top and bottom studs.
Those are my thoughts. Have fun and let us know if you have any questions and how this turns out.