A couple notes here:
Twisted pair wire has a minimal effect on outside interference.
Shielding in a cable does absolutely no good at all unless that shield wire is grounded properly. I doubt that the AC unit is wired for that or their own RJ11 cable would be shielded as well.
Rubber jacket has nothing to do with it either. The noise is probably coming from the ballast itself, not the wire. Can you swap wire on the ballasts? If you can, then you could see if the noise is associated with the cable or if it follows which ballast you are plugged into.
Twisted pair wire has a minimal effect on outside interference.
Shielding in a cable does absolutely no good at all unless that shield wire is grounded properly. I doubt that the AC unit is wired for that or their own RJ11 cable would be shielded as well.
Rubber jacket has nothing to do with it either. The noise is probably coming from the ballast itself, not the wire. Can you swap wire on the ballasts? If you can, then you could see if the noise is associated with the cable or if it follows which ballast you are plugged into.