I'm gering up for production in the winter and was wondering what kind of black and white NEGATIVE film stock you would recommend for the following:

The script takes place in two rooms, one is bright white, the other dark black. You can see that there is quite a degree of contrast. The characer in the white room appears evenly lit, while the character in the black room is lit only by and overhead light and fill to avoid shadows in the eyes.

I was looking at kodak and they offer only 2 film stocks: the 7222 is made for low light situations (we are using 500watt - 1000watt lights) but, from the few samples available, appears extremely grainy. The 7223 requires much more light but is also much cleaner in appearance.

So my question is, what B&W negative film stock do you recommend based on your own personal preferences? please do not suggest reversal, it's out of the question due to requirements.

If you're shooting B&W neg in 16mm expect some grain...

That said, the Plus-X neg (7231) is good although not really fast.

You could use 500T color neg and desaturate in post. This will give a smoother look.

Post isn't much of an option. We only have the developped neg to work with. the problem I have with the 7231 is that it is insanely slow and I'm not sure we'll have enough wattage to light the scene. I'm wondering if there are any other options?

...why? If you're using negative it's either going to be printed or switched in telecine to positive... are you cutting on a flatbed?

We're editing on a Steenbeck. Once we send our film in to be developped, that's it. We can't send in the film for special processing or effects afterwards. Unless you mean to have the film desaturated in the lab when I send it? If so, how would I request for that and at what cost (on average)?

See, we're supposed to film everything practically. We're screening our work prints, nothing else.

You should be able to have a print made on B&W stock from color neg (this is how they did that effect in the old days, AFAIK, or for sequences of B&W in a color film).

Anyway, any of the Kodak B&W neg options should be fine. You really don't have many choices, so you can't be too picky. Select the best for your lighting situation. Double-X is probably good but it has a healthy amount of grain.