I agree that multiple speakers can fill a large space with sound, it the costs usually work out to be the same as more conventional approaches.
One of the challenges of multiple speakers in large single spaces is timing delay, where the sound from the furthest speakers arrives after the sound of the nearest speakers. Added to this are some rather complicated reflections. Most AVRs can correct for this at the seating location but have no way of adjusting as the listening position changes. This leads to problems when listening to 5 channel source material (such as Blu Ray) while moving about the room.
When listening in two channel mode, the smaller number of driven satellites cannot fill the room with adequate sound pressure. They might do a reasonable job up close, but would probably struggle projecting to the back of the room described by the OP.
I agree with your point about LFE for music. A good response down to 30 Hz is certainly adequate for music. It is less so for movies because sub-bass is so frequently used for added effect.
What this says to me is that the OP could either use a combination of multiple satellites and subs -or- floor standing speakers (front channels),satellites (rear channels) and a single sub. Each of these have trade-offs though.
It seems to me like his space doesn't introduce the kind of acoustic difficulties one normally experiences (small rooms, square rooms, low ceilings etc.). It's size, however, makes it challenging to fill with sound for both movies and music at his budget.
This is a tough nut to crack!