Hi Andy,
I concur, theres nothing like towing to seek out the weakness in a cooling system and It is usually the Rad in my experience. You do need to get the whole system checked out though including the thermostat before just diving in and replacing the rad.
I am not a Merc expert but would have thought an E series would have a transmission cooler as standard fit which should be adequte as long as the ATF level is Ok and in good condition.
On the struggling bit - that road over the Central Massive goes up to about 3k metres at it's highest point and a fully loaded vehicle will find it a challenge, hang a van on the back and it will not be sprightly that's for sure.
I drove that route from Spain earlier this year in my old Bighorn, almost unloaded, and she certainly needed some hard right foot to maintain speed.
Modern electronics are suposed to compensate for the effect of altitude but at the end of the day they only squirt more fuel in, if your nocking on your gross train weight then more fuel will just produce more heat.
With tiptronics you can also help things by keeping in a lower gear for inclines - staying in Auto can cause the box to hang in too high a gear which again heats things up a bit.