This is starting to get frustrating...
I used the jarfix tool, which let me know that it updated the jar association to the Java 1.9 installation.
The write up on the tool mentions using to the tool to avoid manually updating the registry, so I did exactly that.
(you're looking for the 'jarfile' entry, for anyone that's curious)
But still no joy.
Meanwhile, I tried entering javaw -jar forge.x.x.x.exe (and also copied it and renamed to .jar) in the command prompt, both complain about it being a corrupted jar, which it's not, because it will work if I double click on it.
Having run out of seemingly reasonable options, I finally gave in, uninstalled my 1.9 JDK, installed the 1.8 JRE, ran jarfix just in case, and Forge is now installing.
Thanks for the help!