it depends on the bedliner. some of that is rubbery and squishy, and that might help absorb MECHANICAL resonance, but maybe not much for acoustic.
then there's the liner thats hard as a rock, that definitely wont do anything.
either way, thats probably more expensive than other options meant for proofing.
I built a quiet office for a plant manager who thought everyone could hear his conversations through the walls. Used the double wall method with a twist. The inner side of the wall had two layers of drywall sandwiching 3/32 lead sheeting and some light gauge Z-strip.We even put lead sheeting above the suspended ceiling,too.You probably can't use lead these days, but that wall killed all the sound transmission and my boss was a happy camper.
Seems like there are a few options for heavy fabric that will function similar to lead as a sound stopper. dB Bloc being one brand name I came across. For the walls it sounds like using the Quietrock and isolation clips to hang it could be a good option plus acoustic insulation. Although the cost of that stuff adds up fast. No problem if we find a good donor though 
I'm not sure how viable a "room within a room" plan would be. It's not a big space and that might make the room too small. Tomorrow I'm off to do more measuring and present all these ideas to the guy who is actually in charge.
the other thing to think of.. hard flat surfaces create echoes. Walls at angles or even built into smaller walls at angle to each other break them up.
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