Great speaker sounds terrible in my room?

If they were from a store sale, call the store. Or return them.

If it was a private sale, then offer the fellow, or woman, a dinner (or something) to help you set them up.
(If they did it once, then there is proof that it worked for them.)

Ten feet from the front wall is way too far! No wonder they appear to lack bass! Try one or two feet instead!

@jasonbourne52 usually I agree with you, but in this case I think that the OP needs to at least consider adding a sub(s).

I base it on this article (page labelled #6 at the bottom and before and after pages.):
 

@holmz Good find! Thanks for this.

@jl1ny  (your question may  have helped me more than it is helping you)

I have been though 25% of the papers (adjacent to that link.)

I think,,, that the best way to approach the problem is with some shift in perspective  to make it a challenge.

Maybe see if you can demo some subs…, if you read the lin, then you know what I would suggest.

They (subs) work vest in the corners, but the speakers pull out from the wall is better for imaging.

And we put speakers near that wall to reinforce the bass…

So a multi purpose room is a challenge, but there may be a lot of existing work that can guide us.

Approaching it as an engineering challenge is different perspective, than it being solely a problem. And likely brings a better mindset for opening up the solution space.

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.