The freighter idea sounds good. For the other dialogue, perhaps:

Sir, Phasma has all available troops searching the cell block, and base patrols are doubled."
“Put every hangar on lockdown! The longer it takes to find her, the more dangerous she becomes.”

And yes, I was planning on fixing the music issues and making it less repetitive. The original film has this musical theme during the update scenes, but now that they’re all together it needs more variation.

JEDIT: The other option to fix the repetitive nature of the scenes would be to restructure the events to be a bit more in line with the theatrical version.

-Kylo finds Rey missing
-Rey runs down the halls
-Kylo Updated Part 1
-Falcon Hyperspace and landing
-Senate Response (cuts to mountain establishing shot)
-Kylo Updated Part 2
-Han, Finn and Chewie
-Hux Starkiller update
-The Crew Enters the Base

The trouble is that Kylo’s tantrum is a natural end to those events, so cutting to Rey feels odd as well. However, it probably makes the most sense to put the Kylo update part 1 scene right before the Hyperspace shot so that when we come back to the base and have a similar scene it’s as if we are picking up where we left off.