Curtis: I worked it out the same way (not knowing American suspended ceiling panel sizes but guessing 4x2ft) and reckoned circa 20ft. That's a HUGE space to work in. Postively acres of space for a bit of proper background seperation. Funnily enough (small world!), I'm having the same discussion with a guy in Ireland who simply will not move his subjects far enough away. We've increased it to 3ft so far - and even that was under duress.
dmward: David, I'm with you 100% over controlling light spread. In our massive
UK rooms (some as huge as 10x12ft including furniture so actually 9½x 7½ft, interesting posing a Bride in her gown), I always used softboxes for this very reason. However, in this instance I was trying to work with what OP has got by describing ways to control what he calls 'light spill' onto his background. I do think he was badly advised over modifiers in this context, but what's done is done and there appears to be an "OP Junior model" around; we know what money pits they can be 
coeng: Unlike seemingly everyone else, I don't think the drape is ugly. It could benefit from a little finessing but I quite like it. We went through the 'Splodge' background phase 10-15 years ago, a bit of elegance (potentially) has a lot to offer for variety. You could, for example, arrange the folds to give implied movement and dynamic diagonals subtly in the background; even accentuate this with a carefully placed gelled background light. Can't do that with a 'Splodge', it's forever splodgy with no other real options.