There are two fundamental issues, in my mind. One is electric fields, which are due to the voltage magnitude, and can be tamed by either your conduit system (aluminum, steel) or simple shielded twisted pair. STP seems much more practical a solution for this.
Second issue is magnetic fields, which are due to the current through the wires. For some tubes, the amperes of AC heating current can be significant. Traditional copper or aluminum shields are ineffective to shield magnetic fields, so you would have to resort to a magnetic shield, such as steel, to effectively constrain the magnetic field to within its boundaries.
Typical alternate solution is to tightly twist the wires, effectively minimizing magnetic field strength outside the wires. Practical issues seem to favor this approach as being sufficient.