So I just watched all of the Indiana Jones films again recently. Great fun as always, and I even appreciated the 4th one better the second time (still my least favorite, though). And of course I couldn't help but think of Monterey Jack and how he's always seemed to be disappointing as a character, at least when you have the expectation that he's supposed to be Indiana Jones. So here's my take on an update. If nothing else, I think adding the "I'll Think of Something" ability would be a great addition. That's one of his main catch phrases throughout the films and one of his best traits; he often gets out of perilous situations with some quick thinking and clever ideas.
Other changes... I removed his two starting Unique Items and reduced his starting money from $7 to $6. So yes, he still has enough to shop for a Unique Item, but he won't have 3 after the first turn. He can obtain them easier now with his Fortune and Glory ability (updated from Archaeology). He also starts at the Train Station... I don't picture Indiana Jones living in Arkham but traveling there to look for some archaeological artifacts in the midst of the Ancient One's arrival. I switched his Lore and Luck around to 5 and 4. Yes, he is incredibly lucky, but a lot of his survival is due to his quick thinking ("I'll Think of Something") and I think he excels more at Lore. And I bumped his Will up from 3 to 4. He's nothing if not brave.
I also felt he should have an Ally, as that is usually the case (e.g. Short Round, Sallah). I might make a specific Ally for Sallah or Short Round and just give him that. All told, he is probably stronger than his previous incarnation, even without the 2 Unique Items, but not too much so, and more importantly, he's more interesting.