It is not a simple problem. The only saving grace is that your cantilever is so short and the beams are well braced laterally at each end. For a small fee, I would not consider the project. For a larger fee, I would want to consider it very carefully before granting the architect his/her wishes.
One method of tackling the problem is to treat the bottom of the web as a compression strut, calculate its L/r and use a bending stress equivalent to the permissible axial stress. To make that work, you would want to use hokie's suggestion of a built-up member with a fairly thick web.
BA
