Great speaker sounds terrible in my room?

I don’t think the basic problem of having poor balance due to insufficient bass will be resolved by changing components. What would really help is to spend about $100 on a measurement mic. and download a free program called REW. This is the only way to remove the guesswork. There is a forum that has a dedicated thread on using REW. It is a very useful tool and can also help you find the best position and set up for the sub you have.

I’m wondering if a single better sub (Rel S510) would be a game changer or make matters worse.

More than 1 sub results in a better distribution of modes. If you take your new found measurement skills 😎 and look at a plot of your speakers in your room you will notice huge peaks and valleys (nulls) instead of a nice ideal flat response. The peaks obscure detail and the nulls rob you of information, this is info containing important parts of the structure of music. It is essentially lost and unfortunately EQ can not bring it back!

Adding more subs will result in many more peaks and partial nulls that serves to smooth the response. The peaks will be lower and the nulls fuller. The more subs the smoother. So try for 3 or 4 and as I explained they do not have to be huge. The REL will reach down low and the additional smoothing-subs will even out the room which you can watch happen on your computer. Using smaller subs will smooth out the low frequencies as well as big expensive subs, they just won’t reach down as low but you will now hear stuff you didn’t know was there. The whole sound is improved and by that I mean the mids and tops with a w-i-d-e sweet spot.

If you have some mates with subs see if you can borrow 2 to just test the waters. If you set them up properly I can assure you that you will soon find places to put them, like behind your sofa. There is much to be found on this on the net. Doing this will be the game changer.

No amplifier, cables or any tweaks will provide you with what I’ve described.

How the hell do you walk around when your speakers are 7 feet out from the wall.....

(Pinthrift girds his loins before posting this)

I've decided to risk the flac that will surely be coming, however, if it helps one music lover during these trying times, so be it.  

My studio is beneath our bedroom and my wife turns in early, during my "prime-time" late night listening.  Lately, my system has been sizzling, at optimal performance.  The better things get, the more I'm drawn to classical, choral and smaller jazz ensembles, often with large dynamic swings in the music, especially with classical.  After my wife is asleep, I can often get away with around 70 decibels.  This is still frustrating with softer classical passages, often losing my interest along the way.  

So, this has provided a nice solution, not perfect, but satisfactory for late night:  https://wwwearglasses.com

...do I feel silly with them on, sure!  Are they comfortable and do they work, sure!  Check the science page.  Yes, there is loss, but at age 75, for their purpose, gains override the loss.  Having the benefit of great electricity here, I still have all day for peak listening. 

Okay, having risked ALL credibility in this Forum now, wishing you More Peace.  Think Positive / Test Negative.  Use laser ruler for setup!  Pin

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...

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.