To update on this: you can purchase PRV rate Night Riviera tickets over the phone as I have done it recently.
As stated above, GWR offer two options:
1. 75% discount off the most expensive Advance-Inclusive package in each type of accommodation (solo or twin) on presentation of a TOC Privilege Card, or
2. Purchase a Priv-rate ticket and pay the sleeping berth supplement. (£55 each if sharing, £80 if single).
Option 1 availability is quota controlled. If no Priv-rate advance package tickets are left, you will need to take Option 2.
This is documented on the Rail Staff Travel website, page 16:
https://www.raildeliverygroup.com/files/Publications/services/rst/RST_Where_Can_I_Go_NSG.pdf
I had originally visited the booking office at Paddington, to be informed that there were no PRV tickets on the sleeper - not just for the night I wanted, but for the entirety of the three month booking window. I have a feeling the clerk was ill-informed. Even if the quota controlled tickets (option 1) had all been sold (unlikely over a three month period) then I should have been offered option 2 above.