I don’t have a magic answer as other unknowns may tend me to take another path. We know that 12VAC has 2x the electric field while the 6VAC has 2x the magnetic field. What is the major pickup circuit, electric or magnetic in your design? We normally twist the heater leads to keep the magnetic fields low and the electric fields are routed away (or shielded) from the grid or other hi z pickup places. For preamps I generally would go for 6 VAC heaters as then both cathodes will tend to have the same electric fields. If the AC pickup is coupling into above the noise floor go for DC heaters.
Duke