As you probably know (though I don't think I know who you are), I used to work at Amsterdam and can tell you, the owners are very concerned about the music in their location. However, Jazz and any other music that would be deemed "soft" would never be played in the later hours of the day. As for attracting a better class of poolplayers, I simply don't know what you speak of. There may be one or two rooms in New York City that rival Amsterdam's clientele and none are better. It may not be like the old Chelsea Billiards but I assure you, the strongest players in the city are now in the upper-westside.
Broadway's clientele has really diminished since the smoking law went into effect and Masters started making improvements to attract gamblers. I went to B'way back in December and was simply disgusted by the cloth that hasn't been changed in over 3 years, the horrendous smell and the lack of good players. There was simply no gambling going on and the only thing I wanted to do was go home and take a bath. It did have an interesting scene back when tobacco masked the smell but since then, they've spent zero dollars on the place and it reeks of it.
Really, there are two rooms in Manhattan. All the others are a waste of time. Some may have a solid table in the front but they only have one or two decent players coming in with any frequency.