'07 6.0L safe max coolant tempurature while towing

Ditto on checking your radiator. This is what the radiator looked like on 99 Silverado truck when I swapped the engine. The radiator was okay, but I replaced it only get the wider version. Truck had 260k and the radiator was original. A pressure wash at minimum is something I would have done to clean out all of that gunk...

IMO IF you are in a hot climate, towing, mountain areas you've hit
the trifecta for upgrading all the cooling...
Get OE or better radiator. Trans Cooling is REALLY important to upgrade here.
Anything over 225* engine would really get me worried..
Over 225* trans temps would get me to pull over or figure out
how to reduce load ...
Now just touching these temps for a little bit is no big deal as long as
it cools off shortly (over the 225*)
Make sure you have an entirely updated cooling system. Your rig is over 15 years
old.. The readiator, water pump, thermostat, etc has all seen better days
You can also change your coolant to a 60%-70% distilled water. Water cools
better than antifreeze, but you need at least 20% for lubrication and corrosion protection

At higher elevation increase the concentration of coolant from 50/50 to like 60/40. This increases the boiling point temperature.