All Canopies Must Die

Yeah, Canopies can be a pain... There are several solutions to your problem I think. First, you can always write to Airfix/Heller and ask for a replacement part. They are pretty good about that (not as good as Revell, but good enough!). For many kits, you can now find special masks that are already pre-cut and specific to a particular model; Eduard is one of the companies producing them. They are a bit expensive I think, but it could help you. Next, you could try liquid masking products such as Maskol (Humbrol), or simply Krystal Klear (Superscale), or even pva-glue (provided you do not let it dry too long, because it can become very difficult to remove by pulling the thin film away - but again warm water will get rid of dried pva-glue anyway...). This last method is much easier than cutting little bits of tape to cover individual window panes. No need to apply pressure so that t paint does not go under the tape.
Hope this helps!