Hi - was perusing the tube threads and saw your post. I have not looked at the 339 circuit in person, you would definitely want to verify that the heater is not already center-tapped and figure out how it is ground referenced (one half is connected to ground in the 336SE). Also, since the 339 has a dual mono supply and the heaters are run from two different transformers, two center taps / elevated supplies would be necessary, one for each channel.
I assume the 339 has similar hum issues to the 336 then?
Looking at the circuit, the transformer heater windings are attached to a small PCB. I would look there, make sure there isn't a center tap in place, cannot see the underside of the PCB.
However, it looks like the heater supply is grounded at the driver tube here, same as the 336SE, the connection would have to be broken when the new ground reference is made.