I think a good way to make an older Indy story work would be if (just bare with me)...
[fan-fiction mode on - story time]
... the cold open was Indy and a colleague of his around the same age making their way through traps, etc. to find the Fountain of Youth. When they find it his colleague approaches the fountain to drink. At first Indy was excited about the prospect but when it comes time to drink, Indy refuses. He only wants the find he says, he doesn't want to have to "go through all of it again, once was enough" in reference to his life. Indy warns him that it might not be all that it's cracked up to be, there's gotta be a catch. His colleague ignores him and goes to take a drink... as he approaches the pool of water it triggers a trap. The whole place collapses with Indy narrowly escaping... his friend doesn't make it out. This bittersweet open leads to the title.
[okay so the movie would not actually be about the Fountain of Youth, that'd be the story we only caught the end of]
... the movie opens and explains whatever it is Indy is actually after. On his journey he encounters, not an army, but a group of pirates or whatever you want to call them that are also after it and are well equipped with guns, etc. They are led by a 20-something young man who has heard of this Indiana Jones. Indy winds up in countless fights and traps, chase scenes and what not as you probably can imagine.
Then he ends up being outsmarted left and right. He cannot get the upperhand. He catches up with the leader and is essentially beaten to a pulp and called an "old man" who is a "fool." In the fight the leader explains his plan to use the Mcguffin to gain world power. At some point while fighting Indy gets a close look in the man's eyes and realizes who it is. He says his name like a question. But the man throws him down and pulls a gun. Indy says, "Whatever that fountain did to you, it's changed more than just your looks." The man explains that, "it's certainly changed more than my looks, it's made me stronger, sharper... I'm actually better than my younger self. I am the ultimate form of human." Indy replies that he has "heard that kind of thinking somewhere before." The man doesn't shoot him but instead decides to bury him alive or some such nonsense. This obviously gives Indy the chance to escape.
Now that Indy knows what he's up against he is more cautious and he meets up with his old friend at whatever the finale locale would be. Temple, Pyramid, pirate treasure of some kind... whatever. At this point they both struggle with each other and there's an epic final scene involving the mcguffin.
Indy is put into another position to save the man or let him die and the man retorts, "Only the good die young, Dr. Jones..." faced with his impending doom. Indy replies, "You're not young. You're ___ years old!" and he pulls him up or saves him in whatever way.
Before they escape, the place caves in on them or explodes or wahtever and Indy doesn't make it out. His hat blows in the wind towards the man and it Indy has finally died. The man comes to his senses and returns to a normal good life and they name the college or a department after Dr. Jones. A few months has passed. Finally we get some kind of hint or teaser at the very end that reveals that Indy didn't actually die but was trapped and it took him obviously a long time to get out and to return home.
[END LAME FAN FIC IDEA - STORY MODE OFF]
... I just think a good young versus old would make for a good story. I also think that having the young guy actually as old as Indy would also make it more interesting. Just a thought. I think this way an old Indiana Jones could work.