[Reece]

I like the idea of the separate filament transformer for the antique CRT. As to the other tubes, you can put an inrush current limiter in series with their heaters. Check on Mouser.com for example for Inrush Current Limiter. They have a high resistance when cold but quickly drop resistance as they heat up and bring on the tubes gently. Don't have the schematic for your set. Are all the tubes in one long series string or is there more than one string across the AC line? You might need more than one ICL. The one I use is Mouser P/N 527-CL90, G.E No. CL-90. It can handle 2 amps and has an initial resistance of 120 ohms, so it's the softest start of them all. But you might be limited by the 2 amp capacity depending on the heater string(s) that you have. Need to add up the amp requirements of all the tubes in each string. The next one down is the CL-80 that can handle 3 amps but is 47 ohms, so a little faster start. These things are all less than 2 bucks each and good insurance. They look sort of like a small ceramic cap. They will get hot so you want to mount them on a terminal strip under the chassis and "out in the air" away from any RF components that might drift if heated.

Reece