I'm in the very early planning stages of a home theater and I was doing a little research on doors. My budget does not allow for thousands of dollars to be spent on doors. I was thinking about sealed Safe-N-Sound doors. Because I have a sump pump in the back of my theater, I will need a second door behind my planned screen wall for access to the pump in addition to the entrance door at the back of the theater. This area for the sump pump will be unfinished, so sound escaping through the door will have very little preventing it from reaching the family room directly above. I plan on using clips and channel, double drywall, green glue. My main concern is sound traveling up to the level above.
My question is, considering the doors are a weak point, is it a waste of time, effort and money to do clips and channel with double drywall and green glue? Will all my other efforts be wasted by the sound escaping through the doors? Because of my door situation, I don't want to invest all that time and money if I am going to see little benefit.