I second what Don just said. Isolation is the key. You can get away with a power transformer that has dual isolated secondaries, but this is a specialty item so don’t bother tracking it down. At the DIY level, just get another B+ transformer that runs at a voltage suitable for the IT-connected driver tube, and take it from there. In terms of rectifiers, damper diodes are the quietest of all, but they consume a lot of heater current at 6.3 volts.
The dual power supply approach is surprisingly rare in consumer equipment, even at extremely high price levels. It is the single biggest improvement you can make to any tube gear, from push-pull 6L6, EL34, and KT88 to SET amplifiers of any type.
Extremely large banks of electrolytics are popular over in transistor land, but they are frankly mediocre sounding caps, compared to good film caps of more moderate values from 50 to 200 uF. In the Karna, I used banks of industrial-type motor-run caps from ASC and GE.
These are precision parts designed for extremely severe duty outdoors. I prefer them to audiophile parts in that application. A minor audiophile tweak is to bypass the industrial array with a single 0.1uF cap of very high quality, such as copper foil. (Also use copper foil for the RC or LC coupling of the 6SN7, but be aware that wax caps are not suitable for under-chassis use.)
Location is important. Keep the wiring, especially in the cathode circuit, as short as possible. This is more important than the type of wiring, although if you want to go nuts, use industrial Litz wire for the critical audio path. Litz does require a solder pot to get rid of the enamel coating, a minor annoyance when working with it. A close second choice is tinned stranded, which is super easy to work with.
This approach, if done right, will take your SET performance to the mid to upper tier of Audio Note, in the $20,000 to $50,000 price range.