What about the floor?

Take up golf for better sound.... hmmmm. What a great idea!

Yes, it affects your sound, but aesthetics and room balance matter.  What I mean is, shag rugs are nasty, so I totally understand getting rid of them, overall balance of the room can be affected by adding treatment elsewhere.  For instance, would you add ceiling panels between you and your speakers?  Do you need bass traps?  Do you have enough diffusion?

Assuming the floor exchange was bad for the room, you can make up for it.

I have a wood floor in my listening room. I got a 4 X 6 oriental carpet and put a non-slip pad underneath. It is a lot easier to change your mind when you have a bare floor to start with. 

I also have wood floor with a large antique Oriental carpet on it. A smidge of damping but not too much.

Suggest that you set up the room with no covering, nd then see if you have significant slap echo (clapping hands in an empty room usually produces quite a bit). Then lay a carpet down and try again. It should prevent or reduce the echo without too much damping.

Don't forget the ceiling.