[DrBrightonone]

I think I would take masking tape and carefully tape off the white parts. Then apply polish and use the brush to buff them taking special care not to knock the tape off the white parts. Once done with that, I might use liquid white polish on the white parts. At this point, what could it hurt? The shoes are already dingy and probably destined for the trash heap if they cannot be brought back to your satisfaction. If that didn't work, I might consider dying the white parts black and polishing the whole thing.