I was in a similar situation recently: a customer's bike had a 4 inch run of metal tubing through the BB for a cable. Old cable came out but the new one would not go in - tube blocked. After trying several things I finally clipped off a piece of old brake cable, maybe 3 inches long. Chocked that into a drill motor then fed that cable nubbin into the tube. I set the drill motor on reverse so that unwound that brake cable. It quickly turned into a long tiny wire brush. A few turns and I pulled it out along with some sand and dirt that had plugged the tubing. I went through 3 or 4 of these until the tubing was cleared out and the new cable slid right thru. Neato.

This may apply to the OP's problem. I hold a couple of old brake cables back out of the trash in case I need another piece for something.