This.Bookshelf does not mean poor quality, it means a type of design. Putting great speakers in an application they are not designed for will equate to poor performance. Loudspeakers are designed for different applications, if you need to house your speakers inside a cabinet, you need to get speakers designed for that application.
Carpet and pad do have an impact on acoustics, but not all that much, when compared to your walls. If you want to cut down on sounds reflections from the floor, just use a thick carpet, the pad won't really have an impact beyond that. From an acoustical point, you need to address the side reflections, where the sound from your front left/right speakers is bouncing off the side walls towards the listening positions.
The jump you can make with the projector is significant. Yes you will have to deal with the fact that ambient light impacts your viewing, but the pluses are significant. If you have ambient light, go with a bright projector, like an Epson, and then enjoy the massive screen!