The length measurement needs to be made on the centerstand, if you have one. It is the maximum extended length, regardless of preload position. If you don't have a centerstand, then have someone measure the length of the right shock as you stand on the left sode and pull up on the right grab rail to extend it fully.
Too short a shock may cause the pipes to scrape in cornering, and also make it harder to put it up on the centerstand. Too long, and it may make it be too tall at a stop, and while it may help make it easier to put up on the centerstand, it may not allow the tire to clear the ground, depending on the tire size.
Your 350mm is about 13-3/4", while 365mm is about 14-3/8".
Progressive Suspension lists the 14-1/4" 1205BG for your model. I would recommend the medium spring option (90/130 dual rate). They can be had in black (DS310031) or chrome (DS222015).
They can be ordered through any bike shop because they are sold through Parts Unlimited/Drag Specialties, which every dealer orders from. Make sure you know the spring rate, as this shock size also fits much heavier 750/900 dohc and CBX.