Diffuse Front Wall? Absorb rear wall?

FWIW, you will almost certainly benefit from moving your listening position another 2 two or three feet from the rear wall. (towards the speakers)

Also if you place more broadband absorbers behind you (closer to the listening position) then it will help you achieve a larger sweetspot and much better articulation in the mid range. Tube traps are narrow band absorbers - so placement is very tricky - unless these are just absorption columns (not the same as tubes)

I would go with treating at least three corners with big broadband absorbers like GIK Tri-traps - 16 to 20 linear feet of these big guys should start to make a difference. Corners roughly double the effectiveness of trapping.

Why big broadband...because this is easy and works down to about 100 Hz even may have a little benefit at 50 Hz. You can almost never get enough of lower frequency absorption - although you can over do it with mid and trable panels.

I find the GIK's tritraps are just big enough that a single 4 foot tall panel will impact sound in a corner very obvioulsy and audibly at a distance of up to roughly three or four feet away. Further than this and the effect is more subtle and you need to add much more than one panel to get a significant improvement at a listening position that is six feet away or more.

I have four or these large panels and it makes a noticeable improvement...I should do more but there is a limit to what I can accept aesthetically.

Alternatively, I built a huge firelace with stacked logs directly behind the listening position which acts as a random RPG skyline type diffuser and a broadband absorber to boot; an extremely effective and stealthy way to cut down on rear wall reflections. This is similar to your idea of hanging a heavy rug on the rear wall which is also a clever idea. BTW - if you can get your rug an inch or two off the wall then it will be even more effective at absorption.

I previously had 4 pieces of RPG omnifussors at the rear wall. Shifted them to the front wall and placed CD racks at the rear wall. In other words, I had diffusion at both front and rear walls. I find this configuration to be better than having diffusion at front and absorption at the back behind the listening position. The sound is spread out more uniformly without losing energy especially in the high frequencies. I already have absorption at both side walls. Too much absorption kills the high frequencies, dynamics and soundstage. Used moderately will yield excellent results.

I replaced the Sonex foam I had with 3 diffusers (each 2' x 4') which I put next to one another along the front wall behind the speakers. My speakers are about 5' out from the front wall. The diffusers increase ambiance and I enjoy the change. It also increases strident sounds. I discovered that Cabledyne power cords cut down a lot of the strident sounds. ASC tube traps also help.

May I ask what fq. range diffuser do you use behind speakers? Currently I have 1 mounted behind each 34 1/2" tall speaker. Diffuser panels are 2x4’ raised 1’ above floor. This design is tested effective in the neighborhood of 3100 hz on up. Does this sound ok (no pun intended)? I'm a little limited with placement being that theres a wall mounted LCD 3' above floor level. 

ASC makes a model called the Martix Panel, designed for the wall behind the listening position, if the listener's head is within two feet of that wall. It provides a mix of absorption and diffusion, so as to not make for too dead a sound. Maggie owners use tall Ficus trees behind their speakers as diffusors, and then there are LP racks which are of some benefit at scattering sound.