Oy vey.
There's really only one way to come at this, at this point; and that is to do a thorough troubleshoot so that you can nail down exactly what is causing your problem.
Step 1: Reset your AV Receiver back to factory defaults.
Step 2: I'm not super familiar with your exact R-972 unit, but I believe it is possible to update its firmware. I also came across a fair amount of talk about it having had some bugs when it first came out - stuff that got fixed with a firmware update. I don't know the procedure for updating the R-972's firmware though.
So...talk to Sherwood and make sure you have the newest firmware for the unit. You can check the firmware version that is currently on yours by holding down the "Display" and "Enter" buttons on the front panel. I'm not sure how you go about updating the firmware, if there's a newer one, though. I imagine it's done through the USB port, but I'm not entirely sure...
Step 3: Go into the AV Receiver's menu and set the Front Main L&R speakers to "Large" or "Full Range" or whatever the name for no cross-over to a subwoofer is. Also set the Center speaker to "Large". And set all other speakers to "None" or "Off", including the subwoofer.
Step 4: Set the listening mode to Stereo
Step 5: Connect ONE speaker - and one speaker only. Start with the Front Left position. Connect one speaker to your AV Receiver's Front Left output. Do not connect any other speakers. Have a listen to just that one speaker, playing all by itself, with that speaker positioned where your Front Left speaker would normally go. Now swap out that one speaker for another one of your Sierra-1 speakers. Same thing - just the one speaker connected to the Front Left output of your AV Receiver, no other speakers connected, and have this 2nd Sierra-1 speaker in the same Front Left position. Have a listen to that speaker in that same spot. Then swap it out for the 3rd Sierra-1.
You just want to confirm that all 3 of the Sierra-1 speakers sound exactly the same when put in the exact same spot, and connected to the exact same output on your AV Receiver. All 3 of your Sierra-1 speakers should sound identical when you just swap them out, one after another, in this way.
Step 6: Now do the same process - ONE speaker only at a time, each of your 3 Sierra-1 speakers gets a turn all on its own - but using the Front Right speaker output on your AV Receiver, and putting each speaker in turn where your Front Right speaker would normally go.
Again, all 3 of your Sierra-1 speakers should sound identical - one after another, one at a time - in the exact same spot, using the exact same output. But try to take note if they sounded considerably different from when you tried them one at a time in the spot where your Front Left speaker would normally go.
Doing all of this, you should be easily able to confirm if one of your speakers has a defect (it will sound different from the other two Sierra-1 speakers, even though it's in the exact same spot, using the exact same output). And you should also be able to confirm just how much the sound changes when a speaker is in the spot where your Front Left speaker would normally go vs. when the speaker is in the spot where your Front Right speaker would normally go.
Step 7: After these tests, if you have confirmed that none of your Sierra-1 speakers has a defect, connect all 3 of your Sierra-1 speakers, and position them where they would normally go - Front Left, Center, and Front Right. At this point, you should be certain that the speakers themselves are all defect-free!
Step 8: Now put the AV Receiver into just standard Dolby Digital listening mode. (I'm kind of wondering if you might have been using the "Dolby Virtual Speaker" or "Theater" or "Neural Surround" mode, or something...)
Step 9: Put in a THX DVD. Not a Blu-ray. Just a DVD that has the THX Optimizer - such as Star Wars, or any Pixar DVD.
Use the THX Optimizer's Audio Tests. Follow the instructions to confirm that all of your speakers are wired correctly, and playing sound clearly.
At this point, you have NOT run Trinnov, and you have not made any changes to the speaker setup in your AV Receiver's menus, other than setting all 3 of your speakers to "Large", and turning all other speakers "off" or to "none". And you're using just the basic Dolby Digital listening mode.
Step 10: If you've followed the above steps in order, you should be able to confirm, at this point, if there is a hardware malfunction. Listen carefully to the static-noise test tones that the THX Optimizer plays. They should sound pretty much the same from each of your 3 speakers.
If you notice a big change in sound between the Front Left, Center and Front Right speakers when you go through the THX Optimizer Audio Tests while sitting at your seat, try moving away from your seat, and sit down more in the center of your room. Just go through the THX Optimizer Audio Tests while you, physically, are sitting more towards the center of your room and away from the back wall.
Doing this, you should be able to confirm if the differences in sound from Front Left to Center to Front Right are inherently coming from the speakers, or if they are more of a room acoustics issue.
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Basically, you just need to confirm that you don't have a hardware malfunction of some sort - either in your speakers, or in your AV Receiver. If you go through these steps, you should be able to pin point what is causing the issue. If you have confirmed that all of your speakers are problem-free, and you are sitting away from the walls, more towards the center of your room, and you're using just the basic Dolby Digital listening mode with no other processing going on at all - if you confirm all that, but the sound is wildly different coming from the Front Left vs. the Center vs. the Front Right speakers, then you will know that there is a malfunction in your AV Receiver. On the other hand, if everything sounds pretty good in this "stripped down" and most basic setup (with you sitting away from the walls of your room), then you will know that your problem is due to something else in either your setup, or your room acoustics.
Pin point the source of your problem first. Then we can discuss the best way to solve your problem. I'm all for acoustic treatments - and the plans you described are perfect for a broadband bass trap - but unless you figure out what is actually causing your problem, you're just chasing your tail, and introducing more variables!
I really hope we can figure this out. But we have to know, first, if your speakers have a defect, then, second, if your AV Receiver has a defect. Follow the steps above, and you should be able to nail that down