Yeah, I think you should go in and talk to them. I hate to sound so awful, but I think that having had a recent stroke would be a mitigating factor and would help encourage them to accept a mutually beneficial arrangement.
(I don't mean that to sound like you should exploit your own health issues, BTW, I just mean that it IS a mitigating factor - and since it's true and you don't need any additional stress, it should be mentioned - know what I mean?!)
FTR, for NY, the SoL on unpaid tax liens is 20 years (same as NJ, BTW - they *DO* have an SoL, albeit a REALLY long one). But I don't know if that applies to business related liens or just personal tax, though.
Just curious: this nightmare ... did the biz go under? Is it possible that you don't actually owe the taxes at all? I know that with the IRS, if you're a sole prop and you go out of biz, it's not that big of a deal to straighten out (from personal experience). I can't really see NY as being harsher than Unky Sam, yannow?