Looking at the replies again, I understand that heavy fabrics and soundproofing sheets will work better than egg cartons.

Those, and the egg-cartons are both great at reducing echo/reverb/reflection of sound waves within a room - they don't reduce the transfer of sound into a room from an adjoining wall.
Thanks, Pedal Wrench.

I can easily replace Linda's louvered closet doors with wooden ones, and/or drape the doors in heavy foam fabrics or soundproofing sheets.