Since the table is going to be fixed-length, you have lots of flexibility to strengthen the support structure. I think I'd make the aprons pretty thick (maybe 8/4) and create a lattice of solid stock with half-lap joints to span the aprons. Attach the lattice structure to the aprons with mortise/tenon or sliding dovetails. Should be no problem with the top racking

If you're going with the L-shaped legs, I'd take @Jon TenEyck's idea a step further and fill each of the corners with a good-sized triangle of solid stock the same depth as the aprons to provide some extra racking resistance for the legs.