JazzGtr,
My avatar is actually my 356, i bought in 2002. I am going to change it to my 345 one of these days. My 356 is very versatile, like the 335/45/55, and as you know with the PJ very comfortable to play. The bigsby works fine, i think on this guitar as well as, Les pauls it is just a subtle affect. the neck is just a little fuller than my '62 345, a little larger than slim taper, but very comfortable, and it stays in tune pretty well, tuning is not an issue, working with a female singer i tune/check tuning between each song anyway. Nice having an L5. As you age sometimes a large body jazz guitar can cause a little discomfort in your shoulder, at least that is what happened to me. i am good for one 45 minute set, so that is really why i started seeking out narrower semi/hollow bodies.
A nice Eastman 16 in 2 1/2 deep, the Guild X 175 i bought in '78, beautiful but 3 1/2 deep, a nice prs spruce top hollow body, the 356, pat martino, howard roberts fusion iii etc. for me the 345 is the grail, but it has increased so much in value that i only record for the family in my home studio with it and my weekly gig is done with one of the above guitars, not normally guild.
If i was younger and had the money back then i would have gotten and L5 CT, i think that is narrow body, just way too expensive at my age. I have always liked the byrdland, but i am really finished buying, but i still enjoy looking.
peace