Boiler making whistling noise (not kettling)...help please!

Hi All,
I am hoping someone on here can lend their expertise. I have a Weil McLain 68 series boiler, installed in my house in 1992. It's been regularly serviced, and runs well. However, throughout this winter, it has started to make a noise that for the life of me I can't figure out. I've had the local plumber out twice, and they aren't sure what it is, either. It starts shortly after the boiler turns out, and sounds like the whistle that your nose makes when you're stuffy and try to breathe out. The noise sounds like it's coming out of the exhaust pipe, and is quite loud, as we can hear it clearly from our bedroom, a floor above and not directly over the boiler. It's not constant, and earlier this winter was cyclical almost like a police siren, where it goes on and off. Throughout the winter it's gotten worse, and the noise continues practically for the duration of the cycle. Once the boiler kicks off, the noise goes through a few cycles of something like a cat making a loud meow...nothing, then loud, then fading. This happens 2-3x after the boiler turns off.

I've recorded an audio file of about 15 seconds of the boiler running, then 30 seconds after it kicks off so give you a better idea of the sound I'm talking about. Unfortunately, it doesn't look like the forum will let me upload it. If there's a way that I can post the audio file, that would be great because I'm sure it'd be more helpful than my blathering.

Any thoughts or feedback would be highly appreciated, and I'm happy to answer any questions, as well! Thank you very much!