It's definitely something to do with palette loading.
On entering the Start screen, the palette-load subroutine(SR) is run for 16 palettes. It exhibits the "de-sync" on flatscreens (causing it to blank out for a 1-2 seconds).
On exiting the Config screen back to the Start screen, it re-runs this palette-load SR and similarly de-syncs.
As the palette for the Config screen is the same as the Start screen's, there is no need to run this SR again. I shifted it up and bypassed it on return from the Config screen. Sure enough, there is no de-sync now.
For other gameplay screens, the palette list is very long, and it de-syncs for up to 5 seconds.
I looked at Blazing Star to see if it did some optimisation but the SR is the same. A cursory view of Blazing Star's stage palettes show it to be about 1/3 less than Pulstar's. I suspect for Pulstar, all the stages' palettes are loaded at the start of each stage.
It may be possible, albeit laborious, to identify which palettes are not used and only load those needed.
And if it is true that all stages have the same palette list, then it might also be possible to load the entire palette list once on stage 1 and be done with it.