OutboundFlight, after I wrote my long post I went back to the first page of this thread and saw you suggest the very same thing, in a briefer way. I thought, “Outbound might like this!” Keep up with our conversations about it if you want because we could always use an extra perspective for problem solving!
The thing is, if we go the route of Starkiller just being a base, then the only thing we know they might be after would be the map.
Poe would tell Leia that Finn worked on the base, Finn tells Leia his friend was taken and that he has to get back to there. Leia asks him to tell them everything he knows. With an edit I mentioned earlier, Poe would know the First Order has the rest of the map already from his interrogation. When 3PO inserts BB-8’s portion of the map, he says it is incomplete and they don’t have enough information to find Luke.
The next scene is the R2 scene, where 3PO says he probably wouldn’t have the rest of the map in his back-up data (in this version he wouldn’t, but this scene would reiterate the objective). Next, Leia and Han talk, and a Resistance officer tells her the recon on the First Order base has come in (they know where the base is now).
The next scene is Rey’s interrogation, where Kylo could remind us again that they have the remaining portion of the map. If we cut the briefing scene, the next Resistance scene would be them getting ready for their mission, everybody running around and such. With no mention of a weapon or that they need to blow up anything, the audience is left to assume they are going to get the missing portion of the map, because that is what the movie has been telling us they are after.
When they hold Phasma hostage, we could simply change the screen to show a starfield map, and we would know that they are getting the map and they wouldn’t even have to say, “the map”!
And like I have mentioned before, we could rearrange some of the X-Wing dogfight shots when necessary, but we could add pilot VO that simply says, “We have to disable their tractor beam!” That’s really all we need to know about the “oscillator”. And the tractor beam has a stronger narrative purpose than just being a convenient weak spot of the weapon.
All of this is with the idea that Starkiller is just a normal planet.