The framing will be inadequate, as it will be coupled. We need decoupled. So IF you want it done right, you'd pull down the drywall and insulation, decouple the framing, re-install the insulation, then two sheets of standard (cheap) drywall and a damping compound.
I would have them do as little as possible, as it should all be removed when they're done.
The R13 will work as well as any of the listed insulations.
The Soundproofing Company