I have a 38' Calif. with 1 3/8" shaft and I would think they would be the same. I use 5/16 GTU.
If it seems like it won't go into the packing nut easily, before you cut the ring, wrap it once around the shaft. Starting at the end of the packing, use a flat faced hammer and lightly tap the packing against the shaft, working around the shaft. It should form a ring around the shaft and flatten the packing a little. Then cut the ring to proper length.
If the nut is the same as mine, it should hold three rings.