There is a tool called "PS3Dec" that you can decrypt your backups;

Another tool is "ps3netsrv" it can run your encrypted backups over LAN. I think you can play it using ps3netsrv+webman mod, I'm not sure; … dump-isos/

EDIT: RPCS3 site Quickstart section, there's another tool called PS3 Disc Dumper, take a look at it.

I don't know if these tools would be useful for you. I haven't used them yet my PS3 is dead.