Dear Tom,There are many good tips on just what you're asking on www.chiffandfipple.com
If those fail, and, if you absolutely positively cannot loosen the plastic mouthpiece, go out and spend a couple bucks on a Susato, which is a plastic whistle that sounds very nice and has a tuning slide. These are very inexpensive and are worth the price.
Very best of luck to you,
Bob Pegritz