After trying everything everyone suggested, everything I could think of, and finally sending the preamp off to Mr. Mottram, the hum, though diminished, remained unacceptably loud. I left the project for a few years and in the interim built an SP9 and an upgrade on an ST 35, both of these were successful and I enjoy the sound they produce. Earlier this winter I skeptically decided I'd try the last option for removing the hum from the PAS 3X, the HD regulated power supply upgrade.
Fortunately, my skepticism regarding the likelihood of a hum-less PAS 3X was unfounded. I now have a hum free, delightful preamp. I also don't have a specific reason for the hum despite careful assembly of the phono, line, tone controls and Tubes4Hifi PCBs, as well as new RCA connectors and an IEC 3 prong AC connector. In short, the only remaining parts from the original preamp were the transformer, knobs, a few screws and the chassis. The transformer is the obvious source of the hum, although, all of the voltages from it checked out within the specifications. Perhaps someone with more knowledge of transformers may have an explanation for the hum.
The preamp is so quiet that when I first connected it, I was certain, and momentarily a bit crestfallen, that it wasn't working, it was almost dead quiet. It does have some slight hum which I can hear if the volume is at 100%, if I have my ear right up against the speaker, and if I concentrate and listen carefully in a quiet room.
It has been an expensive project, but, given I had assembled the original kit in 1968 I had some emotional attachment to it, wanted it right and want to use and enjoy it, which I shall do.
For anyone contemplating a PAS 3X upgrade, I'd recommend using the regulated PS rather than the less expensive PS upgrade. I'll also add that the support available via this forum is much appreciated.