Awesome! If you could experiment with the dialogue tweaks, that would be the biggest thing. At the minimum, that would be enough to make the change work. With that in mind, here is a few things I think could be altered to hammer this idea across.

Two dialogue tweaks. When Rey says it, and the First Order officer says it (the officer could be redubbed).
Color grade the planet to better match how Jedha looked in Rogue One.
The establishing shot of the planet could be altered to where there is a thin asteroid belt around it (sort of like D’Qar), and add lava inside the large canyon that runs across the planet surface (to imply that’s where the crust was cracked open by the Death Star).
We could take an unused arrival shot of Jedha from one of the Rogue One trailers where the U-Wing flies past a giant fallen statue of a Jedi. All we would need to do would be to cover the U-Wing and its shadow with the Falcon. It is a brief shot, but I believe you can find this trailer in 4K so the quality would be good.
Optional, but we could use Michael Giacchino’s exotic Jedha motif when the gang arrives at the planet.

Also, I’m glad you like the Starkiller base idea! With the search for the map being the main McGuffin in the movie, I felt like they didn’t explain it very well, nor did they follow it through to the final act in the movie (instead having R2 conveniently have it in his databank the whole time!)

Another idea I had was to alter the opening crawl of TFA a little. Instead of vaguely describing Lor San Tekka as an “old ally” of Leia’s, you could have it say:

Leia has sent her most daring pilot on a secret mission to Jakku, where a former Imperial cartographer has discovered the missing piece to Luke’s whereabouts…

The idea I want to imply is that Lor San Tekka originally was looking for the first Jedi temple during the days of the Empire (probably because Palpatine wanted to destroy any trace of the Jedi). At some point during his research, he deserted, maybe because he’s from Alderaan and he felt betrayed by the Empire after it was destroyed (this could be why he says, “To me, she’s royalty” in reference to Leia). He stopped looking for it until Luke vanished, which is when he finally decided to complete his search.

This is why the First Order was able to recover a part of the map from the archives of the Empire. You could then interpret Tekka’s first line, “This will begin to make things right” to also mean that this is a way for him to make up for helping the Empire erase the Jedi from history. He now realizes that “without the Jedi, there can be no balance in the Force”.

Some other dialogue changes could be made throughout the movie. Like when Kylo Ren speaks to Lor San Tekka, he could say something like, “The map, we know you finished it. And now you’re going to give it to the First Order.”

Either way, I think it gives the character that legendary actor Max von Sydow portrays some extra depth, despite his brief appearance. It also gives at least some semblance of an explanation for why this map even exists. So many people after TFA were confused by its purpose, wondering if Luke had left the map so someone could find him. We learn in TLJ that this isn’t the case, so having a clearer explanation that doesn’t contradict TLJ would benefit TFA a lot in my opinion, as well as alleviate some of the weaknesses of JJ Abrams’ mystery box storytelling.