Speaker placement: On the rug OK?

Your room is pretty tight. Moving the carpet in front of your speakers will make little if any difference. The locations of your front speakers is about as good as you can get for your home theater set-up. Basically the throw carpet in the room is absorbing the first reflection off the floor which is well in front of the speakers. The reflections off the angled cabinets and the side bookshelf are probably more of an issue than the carpet directly under the speakers. Treating those areas will be hard to do whithout ruining the look of the room. Unless you have a problem with your current sound, I would leave it alone.

Save your money for a projector with a long throw lens and get it in the back of the room (preferably enclosed) and lower your noise floor.

You've been given very good advice by Steuspeed. What he suggests will help your sound alot.

I am not sure I understand Steuspeed's advise. Having the projector on the ceiling closer to the speaker is bad for the sound? So much so that it is worth an extra $5k to get a long throw projector? I'm guessing that the issue is that it is protruding. If that is the issue, I'm thinking the fire place, which is also protruding (Quite a lot more), is a far bigger problem. I am working on convincing my wife to let me take it out since we never really use it as it makes the small 19' x11'2" very hot very quickly. But she is not agreeing :(
What does

lower your noise floor

mean?

I preferred my speakers on the rug when I had floorstanders. Now I have monitors with stands and I continue to prefer them on the rug. Sub is the wood floor though. All are using spikes.

The "noise floor" is how loud the room is with nothing playing.

Video projectors present noise problems because of their fans. Typically located right above your head with little or no sound absorption, they can be quite annoying during movie watching. Money spent on acoustics for the front channels will be masked out by the fan noise from the projector. Address the projector fan noise first, and then move on to acoustic treatment if desired.

Long throw lens options vary in cost per manufacture. Low-end Runco is $1000.00 extra for example.