Absorption at 50Hz and broadband diffusion at the same time?

I need my back wall to be absorptive at 50Hz (cause the distance from the front is 3.44m and I'd like to minimize to effect of my axial mode between front and back), but at the same time I'd like to diffuse the midrange with some kind of RPG type diffuser. Just for absorption I can build a perforated Helmholtz panel which would be 8" (20cm) deep. The problem is that it will reflect mid frequencies straight back to my listening position. On the other hand mounting a Shroeder diffuser will sort out midrange problems but the 50Hz will stay untreated. I need advice. Perhaps I could build a Schroeder diffuser which would be perforated to serve also as a Helmholtz resonator? Or maybe Shroeder at the level of ears +- 0.5m and above that Helmholtz panel up to the ceiling?

what are your room dimensions? perhaps you have enough ceiling space to put the trap there if you don't have enough floor space...