No, sorry. None of the listed establishments have a private room, at least to the best of my knowledge. I do know, however, that Hennessey is good for renting out the whole restaurant given you meet their requirements i.e. number of people attending etc.
You can also try contacting
The Wallflower on Main and Broadway to see if they can rent the entire restaurant out to you. I have been there many times for larger groups and they have been very good at accommodating us. The venue is small and intimate enough to have a good time with 15-20 people however I have never had to rent the entire restaurant out. The bar staff are a lot of fun and the food is not bad for the price you pay. Drinks are cheap and premium liquor is available.