Mineral Wool or the Roxul Safe'NSound product sounds like a great solution with excellent sound absorption and high resistance to flame.
However, it looks like that stuff is insulation that is to be installed between the studs of the wall. I would consider that a last resort as I don't really want to tear down two or three walls at this point (trust me I've thought about it.
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From aversfi's link, I see that porous foam type tiles like I bought are broadband absorbers. I have no idea what the noise reduction coefficient is though because it wasn't listed. Considering I got 16 tiles for $50 they probably aren't that good, although they do help somewhat.
When I first started researching this stuff I came to the conclusion that I need acoustic tiles with an NRC of 1 or greater for max effect. I'm sure Auralex or the like would have something that could work for my application but I'd bet it will cost 10 times as much as the acoustic foam I got from PartsExpress.