Hi all,
I had theorised this would be possible for a while but I decided to pull it off today just to check.
Blaze1 can use her Star in such a way on the screen with all the Dicks that it opens up the next screen before killing all the enemies. You can then get into the Arcade cabinet / move on to the next screen and load the next set of enemies.
In this video, it appears as though of the two Dicks I left behind, one followed me through into the next screen (lol) and one I guess was still up in the arcade room and got caught. The Galsia also got confused about his spawn, and when I went back to collect them it had locked the LHS screen.
You may be able to fix it theoretically if the Star can reach into the arcade room but I was clearly too low down to try that. Anyway, enjoy the video for science.