lol hi, welcome to ducati life. the bike is hot.
suggestions:
MAC radiator
water+water wetter or engine ice
wire a fan switch to switch on before it hits 217 degrees
remove cats from stock exhaust (email Phl i believe)
fuel module (some say bike runs lean, some say rich. if its running lean though, its going to overheat faster)
the thicker race or comfort seat helps a tad. my ... doesnt nearly get as swampy anymore
move up north
move faster/stop less
you mentioned the bike struggles to cool even when off, get you a halfway decent fan and leave it in your garage, if i come home on a hot day and the bike is running 225-230, i always park it in front of the fan and leave the garage cracked and fan blowing thru the engine block to cool it down a bit quicker.
theories:
you're sitting on a 200HP motor with the exhaust from the rear cylinder running right underneath your ... while the giant piece of metal you're sitting on is bolted directly to the rear cylinder head. it doesn't take a degree in thermodynamics to understand that its gonna get quite hot riding this bike. also, theoretically doing all the mods i mentioned won't help a bit. ¯\_(ツ)_/ ¯ YMMV
the bike isn't meant to sit in traffic on a hot day in southern weather. get out of traffic and to the fun roads as quickly as possible, and if you think you're going to be stopped more than 45-60 seconds, shut the bike off.