Untwisting the line works a treat... but inevitably you will still get a twist at some point.

one thing that works real well is to take the blocks in the tramp out of the system and swap them with stainless rings. But if I understand correctly the halyard is catching on the grommet in the tramp... take the grommet out and just pass it though a reinforced hole. you will need a saddle and ring to take the load of retrieving, otherwise you'll rip your tramp in half in no time.

Few Pics to describe it (the tramp block you see have been replaced with SS rings)
Actually.... how do you put images up here???