An idea from running electrical cable through conduit. Use the old cable to pull it through if it wasn't already removed. Since by your post it sounds like it was already removed, you might try putting a cable through backwards. It might be easier to hit the the hole by the bottom bracket. Then use that cable to pull the new one through in the correct direction. I know they have tools/snakes for that purpose in runing cable through conduit. Perhaps there is something similar to do the same through the chain stay.