Solder harden the portion of the cable that's not supported.

Mark with a magic marker where it exits the sheath. Heat the cable just as yo did to solder onthe clevice (orthreaded brass fitting) Wick solder into the cable. don't overfill the cable and make a bump... it'll bind.

The solder hardened cable will be just as stiff as a solid wire pushod. where its not hardened... it'll still snake through the sheath around obstacles (like the fuel tank). Best of both.