With my idea that they are going to Starkiller Base to get the other half of the map, I figured that since it is the main MacGuffin of the plot, we didn’t need an exposition scene to explain what the new plan is. That scene is really there because at that point in the story, the focus of the plot takes a complete right turn from finding Luke, to destroying Starkiller Base. But, if Act 3 maintains its focus on finding the map to Luke Skywalker, a scene explaining this drastic plot change isn’t required. So instead, you would just have to make small changes throughout Act 3 help maintain that focus.
For example, one idea I had was that when Kylo was interrogating Poe, he would mention, “The map to Skywalker, we have the rest, recovered from the archives of the Empire”. He says this to Rey during her interrogation, but by having Kylo also say this to Poe, it not only gives Poe and the Resistance that crucial information, but we also inform the audience of this fact twice in the film. So, when Han and Finn go to Starkiller Base, we already have an idea of why they’re having to go there (beyond rescuing Rey).
During the Starkiller Base mission, you would cut all references to the shields, and instead they use Phasma to download the other half of the map. You would change the on-screen graphics from the shield being lowered, to graphics of a star map.
The oscillator, in this new version of the film, would function as a planetary tractor beam, and you would set this up a few times through new off-screen dialogue, as well as new on-screen graphics.
For example, the shot in the Starkiller control room, where Hux says, “Begin charging the weapon”, you could create new officer dialogue that says, “Activate the planetary tractor beam” and replace the sun-draining computer graphics to show/hear the tractor beam energy bar loading up (similar to the graphics we see in ANH when Obi-Wan lowers the tractor beam).
I’d assume Rey’s escape would be the reason why they activate the tractor beam, that way she can’t escape even if she found a ship. You could reuse some of the Resistance base cutaways to establish that they know it has been activated, which compromises their mission. It could be something like this:
Connix: General, are you seeing this?
Leia and Statura turned their heads.
Alien Officer: They’ve activated their tractor beam. Now they can’t escape. [new dubbed line]
Wide shot of Leia and Statura
Leia: Send them in!
Statura: Give Poe full authorization for attack!
Comm. Officer: Black Leader, go to sub-lights on your call.
You could even have an X-Wing pilot mention the “tractor beam” off-screen at some point during the battle. My point is that you can establish the new function of the “oscillator” throughout the film without really needing the briefing scene to explain the new plan. Even after they blow the oscillator up, you could have an insert shot of a First Order computer and see the tractor beam energy bar drain. The biggest issue would be cutting around shots of the planet blowing up, which I have seen done to an extent, like in DigMod’s edit, but you would need to find/make shots of the Falcon and the X-Wing squadron leaving the planet without it blowing up around them.
Another issue you run into by cutting the super weapon and sun-draining aspects is when the sun disappears during Kylo and Han’s scene. Perhaps you could replace the fading sun with a moon, and we could see a Star Destroyer pass over it, blocking out its light. This way you still maintain some symbolism of the First Order’s influence corrupting Ben, snuffing out his light, basically. Also, after this scene it is basically nighttime on the planet, so the moon being present could also help establish that it is night now on Starkiller Base.
Anyway, you might not need any of this, but I think this idea could work if a few new shots and lines could be created.