I agree with Deep333’s analysis. You have a couple nasty room nodes - eigentones as they are formally called that are likely at the root of your issue. Seeing as you can’t realistically pull the speakers into the room, and damping them is not feasible, you need two things: first, a speaker intended for half space placement- up or almost up against the wall, and that means a very well damped bass tuning (low Q like .7). Most small speakers are tuned with Q of closer to 1 or 1.1 to give a mid bass bump to camouflage their limited low bass (LS3/5a’s, I’m looking at you). Also, Make sure the speakers come with bungs to plug the ports, allowing you to tune the bass somewhat. I would look seriously at the Monitor Audio Silver 50 7G, The build and driver quality are a definite step up from most speakers in this range, and MA even specifies a 15 CM (6") space to the rear wall as all that is necessary - by design. The 7G MAs all have a quickness and clarity to them that is very surprising, without the usual hardness that can accompany the perception of speed. My second choice would be a pair of used KEF LS-50s - definitely a nearfield monitor, they didn’t spend over a decade on Stereophile’s Class A (Limited LF) list for nothing. They were, and are, the least expensive speaker on that list by a factor of about 10.
I would also, if at all possible, spring for a couple 2X4 ft 2" acoustical panels, They can’t address the LF room nodes, but they will do a remarkable job of clearing up the sound over all. Place them vertically along the side walls at ear level or on the ceiling, centering them on the line of first reflection, e.g. in a 10 ft room, assuming the speakers face is 1 ft from the wall and your listening position is 2 ft from the back wall, the panels would be centered on a line 3’5 ft from the wall behind the speakers.