I'm pleased to say that I now have (once more) a working BBAlerts app on my replacement Pearl.
How? With a bit of help (well quite a lot, actually) from here:
While I don't normally have anything to do on principle with utilities that "crack" installation codes, bear in mind that the BBAlerts developer and vendor were happy to supply new codes FOC for moving the app from one BB to another until support for the app ceased. So I'm not depriving anyone of revenue.
Hopefully the link may help anyone else in the same situation with an unsupported app.