Okay, same basic set-up as "All Good Things..." I'd only have Picard bouncing through time. Three time periods, the NextGen "present," thirty-odd years past TNG, and shortly after Star Trek VI. In the "present" and "future" Picard is Picard. But in the past, we have a Quantum Leap idea, where Picard replaces the Enterprise-A helm officer. Things progress in the "present" and "future" as we saw in "All Good Things..."
In the past, however, things go very differently. The situation flares up in the Devron system. Kirk is ordered to respond, and Picard with his foreknowledge tries making suggestions as how to proceed. But Kirk, thinking of Picard as a lowly lieutenant, is content to ignore Picard and listen to Spock's counsel. So, Picard goes to take matters into his own hands. Spock notices that Picard is up to no good, Kirk and Spock catch the drop on him, and Kirk is going to have Picard thrown in the brig for sabotage and mutiny. Picard realizes he has to tell them that he's from the future, that he must violate the temporal Prime Directive. Picard tells them, but Kirk doesn't believe him. Picard says that Spock knows him the future, that they've mind-melded, and that with a simply mind-touch Spock could verify who he is and what he knows. Spock is dubious, but performs the mind-meld, and sees in Picard's mind the traces of their mind-meld in "Unification" and the veracity of Picard's story. So, Picard isn't thrown in the brig, and we proceed to the three ships in the temporal anomaly.
Here, I would raise the stakes. Not only is the fate of humanity in the balance, but the fate of the whole universe is at stake. In the past, the Excelsior arrives to provide back-up to the Enterprise. The three Enterprises enter the temporal anomaly to close it. But further in the future the anomaly is more powerful and more destructive than it is in the past, and the future Enterprise must withdraw. Then the Enterprise-D pulls out after shrinking the anomaly even further. It's down to only the Enterprise-A.
Kirk is bound and determined to hold it together, but the ship won't survive. The Excelsior closes in and begins beaming off all non-essential Enterprise personnel, evacuating the ship. We get down to the bridge, and Kirk knows that only one person is needed on the bridge to hold the ship together and close the anomaly. Spock says it's only logical that he remain behind, but Kirk won't have any of that. It's the captain's duty to remain with his ship. Spock is beamed away, and Kirk is alone on the bridge, at the helm, controlling the deflector blast into anomaly. The anomaly contracts too quickly, and the Enterprise-A is crushed. Kirk has saved the universe.
Kirk goes out on the bridge of his ship, the fate of the universe in the balance. A better end for Kirk, and a cooler story than fighting on monkey bars.