I know there is a ton of information about repacking stuffing boxes but I was hoping that 310 owners can tell me if they use 1/4" or 3/16" packing material. Mine currently has 1/4" GTU but at the time (9 years ago) I remember the diesel guy who repacked it said 3/16" would be better but was not available so he used 1/4". Can 310 owners tell me what size they have used successfully? Thanks.
I noticed your post has had some views but no answer yet. You most likely have a 1" shaft, which, in our experience, uses either 1/4" or 3/16" flax. The size is determined by the box that was installed. All Catalinas have great owners associations and the C310's is right here, where you could obtain a manual for your boat. Catalina manuals are superb and mine, at least, has a great section on stuffing boxes and includes the size. Since yours is hull #1, I'm sure the manual would be "right" for your boat! 
I have 2001 Hull#57. I use 3/16, had tried 1/4 but found 3/16 worked better and was easier to install.
Was able to check the original owners manual from 1999 and on page 57 it states that the packing should be 3/16" (for some reason it states 3/16" x 3/16"). The page is attached. Once again this proves "if all else fails, read the directions!"
I’ve done mine twice now, 3/16”, but only two pieces. There might be room for a third, but that’s what I pulled out. Minimal dripping, runs cool, very smooth surface.
I did mine with 2 pieces 3/16 no issues the idea is to have it drip you are trying to keep it wet so it will keep it cool.