It is always going to be a compromise Martin, it is a living space with kitchen/dining attached after all, not a dedicated listening room. With the odd room shape, you would do well to consider how you can create a pseudo-symmetrical listening environment before dwelling on room-modes IMHO.
The points Stephen made are valid both on the limited number of panels you envisage and the issue of harmonics.
In these cases predominant attention is on the fundamental resonance (mode/bass trapping) before looking at the harmonics which broadband panels can and do moderate.
Remember that modes and harmonics are amplification of the room, notably in room corners and in your/my case behind the seating.
I stuck up broadband panels in all four corners, and behind and above the settee, which created a balanced environment.
Do the modes still exist? Yes but at low level. Are they intrusive? Not until I really crank it up.