If you have the V-10 then you have the medium sized trans cooler, the 7.3 EXs had the small ones and the 6.0 rigs got the nice big ones. Between the radiator cooler and the air to oil trans cooler you should be OK, we have towed 30k+ miles on our stock v-10 cooler and only been over 200 degrees a couple of times briefly. If you want to upgrade to the 6.0 cooler you should be fine, expect to see cooler temps but I doubt that you will suffer any issues from over cooling with it.
Changing the gear ratio will not affect the speedometer reading as the speedo gets it's signal from the ring gears tone ring, so the speedo only reads axle/tire revolutions, gears don't change that reading. changing tire size will affect the speedo readings and to an extent can be corrected by computer recalibration.
All EXcursions came with factory trans coolers, only very early '00 models lacked the cooler in the radiators, if you have that setup you would benefit from a radiator upgrade, it does a lot of the cooling work.
All Excursions also came with the rear receiver tow hitch, it was part of the federal crash gear required due to the EX being a station wagon vs a truck. EXs with the "Heavy Duty Towing Package" actually didn't get much in the way of upgrades, same hitch, springs, radiator, trans cooler and engine output. What you did get was the larger extendable towing mirrors and on later rigs a rear sway bar, the package was available with both the standard 3.73 or the optional 4.30 (this is for the V-10 rigs only, all PSD EXs came with 3.73 gears) gear ratio. I agree that if upgrading from the 3.73 gears don't go to 4.10, go to AT LEAST 4.30 if not 4.56 gears. These motors make their best power at higher revs so they love deeper gears. I ran my V-10 EX with 4.88s and stock sized tires for 2 years and it towed like a locomotive! I now have 35" tires (vs the stock 31.6" tires) which gives me the effective 4.39 ratio that still tows our 11,000lb TT very well.