Another evening of mining. I used the Dremel, as well as working the epoxy with a old flat bit in the soldering iron (this was a good suggestion, thanks Kenny). I'm now thinking I may have done enough. I've removed all of the carbon and enough epoxy that I can see clearly where the failed capacitor used to be, and clear PCB below I can also see the top of the neighbouring capacitor.
With access to the capacitor contacts I have confirmed that the short is gone, and that all of the diodes in the bridge are functional. I'm thinking that I can do an initial test as is this weekend, and solder another cap in parallel before back filling with epoxy if all is well.