Here is the MDAT File...
Assuming you did the calibration correctly, then the tests were done at a level that is way too low. The graphs are showing an average level of around 65 dB: It should be about a hundred times louder: 85 dB. At such a low level, there's not enough dynamic range left for REW to be able to give accurate results. So I'd suggest repeating the calibration process for setting the SPL level (using your own hand-held meter), then do the tests again with levels of around 80 dB for the individual speakers, which should give you around 86 dB for both speakers, as seen on both the REW meter and also your own hand-held meter ("C" weighting, Slow response").
possibly turning the speakers on their sides
I'm trying to download the manual for those things, to find out how they are supposed to behave, but all I'm getting is blank pages!. But they do seem to be somewhat large for that room.
so that the drivers are stacked on top of each other,
Does the manufacturer mention that it is possible to do that? The manual should tell you. Not all speakers can be turned sideways, and indeed even the ones that can be, seldom should be. Your NS-10s, for example, are lying on their sides, which is a common error with that type of speaker, especially with a console that is reasonably wide, such as yours. Even small head movements totally distort the perception of the sound field. The NS-10s should be standing up vertically, as they were designed to do. It might be possible to turn those Tannoys sideways, but I would check with the manufacturer to find out for sure.
this would also bring the listening position significantly closer to the front wall.
Not necessarily, and with the design of those speakers, probably not. Where is the acoustic axis of those things? How are those speakers aimed? Where is the intersection of the axes, in relation to your ears? Is that diagram you posted of the studio layout back on August 10, accurate and correct? If so, please add the speaker axes to that, and re-post it. Or better still, post the actual SketchUp file, with the axes added.
I'm suspecting that the 116 Hz dip is probably modal. IF those dimensions you gave are correct, then this is the area around that frequency:
111.1 hz 3.9% 10'2", 5'1", 2'7" (2,2,1 Oblique)
113.7 hz 2.2% 9'11", 4'12", 2'6" (3,0,1 Tangential)
118.0 hz 3.6% 9'7", 4'9", 2'5" (3,2,0 Tangential)
118.1 hz 0% 9'7", 4'9", 2'5" (0,3,1 Tangential)
118.7 hz 0.5% 9'6", 4'9", 2'5" (3,1,1 Oblique)
120.0 hz 1% 9'5", 4'8", 2'4" (0,0,2 Axial)
I'm guessing that it's actually the 0,0,2 axial mode you are seeing there, which is related to the vertical axis of the room (height), so modifying the rear wall is not going to help much. All of those (except 118.0) involved the ceiling, and all of them as the first or second harmonic. I suspect the ceiling.
At my mix position it is around 114hz, and as I roll my chair back to the rear of the room, it goes up to around 200.
That isn't evident on the graphs at all. 200 Hz doesn't change at all for any of the readings for the 9 and 10 foot positions as measured by REW. I loaded the impulse response files into REW as well, but they are highly suspect: they claim to have been taken at a level of over 150 dB!

Somehow, I doubt that is true!!! I had to adjust them down by 84 dB to get them to the same level as what was measured by REW. They also suddenly crash down to nothing at 2 kHz, which is also highly unlikely. How were those measured?
But even though they are suspect, even they do not show any changes at 200 Hz. In fact, 200 Hz is about the most stable and consistent point across all of the graphs! So I don't understand why you have the impression that 200 Hz has a null at any of those locations. Maybe you did not have the mic at the same height as your ears when you measured?
The angled grey sections of the ceiling are .5" mdf panels filled with ultratouch and pink fluffy.
Why? What is the purpose of that? 1/2" wood over a 1" - 4" gap will, indeed, give you major absorption in the range of about 150 Hz to 80 Hz, give or take a bit. That's exactly in the range where you are seeing a major null... Hmmm....
said that it would serve 2 purposes. 1. breaking up the floor to ceiling modes in that area,
It's way too small for that, and in the wrong location too. Modes are at low frequencies, meaning large wavelengths. Waves pretty much ignore objects that are significantly smaller than their own wavelength. At 116 Hz the wavelength is 9.7 feet long, yet that device seems to be only a few inches across: hence, it is doing nothing to the modes. Modes are big problems: they need big solutions.
2. serving as a low mid frequency absorption. I think it functions as a dampened membrane?
Yup. It sure is doing that, apparently! And is probably tuned rather tightly, perhaps to the problem frequency you are seeing.
I can dig up some pictures of the construction if it helps.
That would be great, yes! ANd if you have photos of how the rest of the room was built too, that would also help. Especially the soffits.
The original plan was to use those panels to mount these diffusers.
It's not clear at all what theory those are intended to operate on, and there's no useful test data on the web site, so I would DEFINITELY skip those! Whenever a manufacturer of acoustic devices does not publish test data from a reputable independent acoustic laboratory, one has to wonder why.... The question comes to mind: What are they afraid of? If they were confident in their products, then they should have no problems in getting them tested. The fact that they don't, leads one to wonder....
Don't get me wrong! I have no doubt that those things do diffuse: But then again, so does ANY piece of randomly warped material. The question is not "Do they work", but rather "How do they work?". If there is no theory, no peer-reviewed paper, and no independent test results, then I would just walk away from such a product.
but I'm looking into other diffusion elements that will hopefully be more cost effective, and possibly more visually appealing.
But be careful about tuned diffusers in that room: it isn't big enough for most types of diffuser, especially ones based on number sequences.
Assuming that my problem is being caused by low frequency reflexions from the rear wall coming back to the listening position.
I am not at all convinced that your problem at 116 Hz is related to the rear wall. I suspect the ceiling, and most of all I suspect those wooden angled thingies...
it seems like in order for the hangers to be effective, they need to be combined with some sort of limp membrane absorber on the rear wall?
Not really. Hangers work down to fairly low frequencies, and they do not need membrane absorbers in order to work. They work fine all by themselves. A membrane absorber may help, by providing additional absorption at a specific frequency, but it won't help the hangers do their job.
And for hangers, would this sound board material be appropriate for my application?
No. Way too heavy. What you need is something called "homasote". It is a very light weight, low density fiber board product, of the type used to make bulletin boards for use with push-pins (thumb tacks). It is soft and a bit flaky.
- Stuart -