Janie: we architects usually have to consider two aspects of acoustics: transmission of sound between rooms, and reverberation time (RT) within a room. It sounds like you have problems in both areas, but perhaps solving the RT problem will decrease the need to speak loudly, and then maybe the transmission problem won't be so bad.

Transmission is decreased by using heavy material in the wall and by having no openings in it. Sound can only move through a wall by creating waves in the material the wall is made of, i.e. by moving the material slightly. Moving heavier material uses up more energy, so less gets through. But if there are openings, even small ones, the sound will go through those freely. So a louver is a big problem, of course, and foam over it won't reduce sound transmission much because it's light and doesn't use up much energy. Gypsum board over it would reduce it much more, as long as it's sealed tightly to the door, but you'll be losing your ventilation; also, if that louver is your return-air grille, you'll be losing your heating and cooling. Air has to be allowed to leave, to make room for heated or cooled air to be blown in.

Reverberation means sound bouncing around in the room as it's repeatedly reflected off the surfaces, before it's eventually absorbed into the walls, either to pass through to other rooms or to be dissipated by the mass of the wall. The more times it bounces, the longer the RT. Very long RT is called echo. RT is decreased by using sound-absorbing materials on surfaces in the room, and it's decreased more as the area of sound-absorbing material increases, and also as the absorption rate of those materials increases.

Thin cloth has a very low sound-absorption rating. My guess is that it won't have much effect, even if you drape it over all the walls. Covering as much of the extremely reflective marble as you can will help a lot. What about the ceiling? If it's plaster, which is very reflective, can you glue acoustic tiles to it? Those have a very high absorption rating, and they're cheap and easy to install. That should have a big effect. And maybe glue them to wall surfaces, at least to the upper part of the wall.

By the way, the highest absorption rating any material can have is 1.0, which is defined as the absorption of an open window. So leaving the window open would decrease reverberation time more than anything you could put over the window, and it might solve the problems you might create by covering the louver.