We pull a trailer with about the same weight that you have posted aboot. Our EX is a 4wd, we live out west, mountains, hills almost all the time. We have no problem with the 3.73's!!! Yes you can pull in OD, yes you can let the computer do the thinking if you like. I have been pulling fully loaded with 2 different trailers for over 4 yrs with the EX. It has handled everything thrown at it.
Previous tow vehicle was a '99 Suburban K2500 with 4.10's. My opinion is that the EX with the 3.73's actually performs better than the Sub.
We have pulled over 9000 ft passes with it, although we weren't passing anyone, but I'll bet the 4.30's wouldn't be either!!!! I generally do the shifting as the grades dictate, and usually can tell when a downshift will occur before it happens. One thing is to try to keep your speed up as much as possible and shift early to help with that. Once you get dropped too low you will struggle to recover the needed speed.
Now I will say that if some extra cash shows up I will consider 4.30's or even 4.56's since they are better overall for towing. But give the 3.73's a try for awhile before spending the cash!!