Until you test, you have only speculation, no hard knowledge.There are, however, some tell-tale signs...Are there splashes on the ceiling over the stove which do not easily dissolve in water?

If you have the money, i would do that plus add a metal z channel going opposite direction of the joists ( screwed on top of the existing plaster ) and then add another layer of drywall. the Z channel leaves a space that helps in sound transmission. the problem is the sound is transmitted through the existing floor joists too, so just the insulation will not do it because the joists are still against the ceiling. this is something similar, but in this picture they used clips in combination to hold off hat channel from the existing ceiling which will lower your ceiling about another inch. 

A lot will depend on how easy it is to fish wires through the ceilings and walls.

They ran some of the ductwork in the basement, which has an unfinished ceiling, between the floor joists - maybe you could do that?

They completely overlooked the 7' ceilings throughout, steep shallow staircase, and minuscule master closets.

@Sharath Kumar - oh no...popcorn ceilings.

Also, there's a wet spots on the ceiling 

Other than all that, everyone likes a killer home theater or a 3D video wall & ceiling in a night club (ever been to The Fremont Experience in Vegas?).

Hard to tell exactly how deep it was but let's assume ceiling is 8 feet and there wasn't more than 2 feet between water level and ceiling.

Originally our idea was to vault the ceilings but it would've cost too much to do so.