Hi Paul,

Steve is absolutely right ...

can't you derive your pot supply from a separate IC Regulator and filtering caps. a 78L05 or LM 317 L ( better to use: Zout smaller !!! ) could be sufficient here.
There's margin between 30 v and 5 v ... a very low pass R-C filter ahead the regulator could help further.

Using an op amp as a low pass filter ( sallen and Key i.e ) close to the pot to lower glitches catching on the line is to consider too.

THE Rich solution is to fully separate PIC and 6203 supplies from mains and use opto-isolation. The surest solution too.

Driving 7 segments Leds is also a funny sport, in this way. Beautiful spikes too.

Alain