I’ve not encountered the pilot lamp issue previously. The artificial center tap should have no impact on the heater circuit (other than to help make it balanced and quiet).
As for the fading in and out and crackling, I would start trouble shooting by using a chop stick to carefully poke around the circuit and see if you can find a loose or marginal solder joint. Pay particular attention to the tube socket lugs and areas that heat up and cool down. Double check all the solder joints in the heater circuit. When the sound fades out, are the tubes still on (filaments are still glowing)? Post some pics of the chassis if you can.