Hey Tom... yur on the right path...
... IMHO...
Removing the grid work from the side vents allows about 30% more air to pass through...
Removing the raintray allows the heat to vent straight up, especially while in traffic, and evacuate heat from the bay quite easily... so much so... I have taken the LEFT vent and using a 2 1/2" x 3' heater duct... sawed off the stock air cleaner snorkel and connected the two for a FRESH air, as well as a bit of a RAM air intake. Simple, effective, inexpensive, appears stock, works exceptionally well.
As for the remainder of the cooling issues... I too flushed and "rodded" my own radiator using pool acid and replaced the stat and cap... using Stant products, 13 pound cap (18229 or 28229) and a dual action 180 degree stat (45378). My engine runs at 185 degrees all the time while MOVING and the fans ONLY come on during summer months in LA traffic, cycling between about 210 and 185 degrees... and I mean CYCLE, as in on and off.
I also connected an override switch which I use in WINTER months just to exercise the fans... and I said fans, 'cause I have two, one that I installed off another Fiat and wired in PARALLEL with the first fan... with NO upgrade in fusing. Works just fine... for over 10 years now...
Note I also live in the high desert... but I am told I live a CHARMED LIFE... Hopefully your life will soon be charmed also... Good luck.