Glenn of course is right. There is no question addressing bass problems, which you will certainly have, will improve the sound of everything considerably. Unfortunately bass traps are large and not cheap.
The items you linked to on Amazon will only help with higher frequencies and then you have to place them correctly. I would be more confident of buying something from GIK (I have bought from them) or perhaps Real Traps. Both will give you good advice.
Glenns fourth link is worth listening to. Apart from the obvious echo some of the bass notes seem missing without treatment. With treatment you get all the bass notes at the same dB level. That's what really happens when adding enough bass traps. They remove the bass the room is adding to reveal only the bass from the music at your ears.
Moving your piano, speakers and listening chair will change the sound you hear (both lower and higher frequencies) and may improve it to a degree. So will altering the toe in of the speakers - pointing them more to your chair will presumably give you more sound direct from the speakers and less from the side walls. Experimentation is the key.
If you don't want to spend money then you should start by filling the room with soft furnishings. At the moment it must sound more like a bathroom then a living room. Just to get an idea you could temporarily put cushions/pillows/duvets where you think the sound reflects off walls to hear what happens. Only higher frequencies will be affected though.