Try downloading a copy of REW (Room Equalization Wizard), select the Room Simulation tab and enter your room dimensions. You can then move speaker and listening positions in the resulting diagram (you can do more, e.g. change surface absorptions, but this is the basic capability) and see the simulated frequency response up to 200 Hz.
Very educational and a lot easier than actually rearranging the room...
While I generally agree, in the case of the OP, they have few choices.
Secondly most speakers image better when the early reflection are more delayed.
I think going by ear is their best method for getting the speakers in a good place, but that will do nothing for bass if they do not couple to the wall.
So the only option remaining is a subwoofer, and at that point the REW makes sense.
With the difficulty in getting subs to play with music, and being a bit biased towards Vandys, I know what approaches I would be considering. The new ones are supposedly very good, and the older models will likely be appearing, and they are good too.
but I totally agree that a measurement is a more optimal way to convey the problem with the sound. And that the sketch the OP provided an improved way to convey the room constraints.