Brass music - Dummies Guide to changing playback to E Flat ?

In MuseScore the playback pitch (concert pitch) is the "holy reference" of the note. You can't change it without affecting notation in one go.

What you can do is:
1. Change the Bb instruments to become Eb instruments using "change instrument" from within their staff/part-properties
2. Transpose the score to counter the transposition introduced by using differently transposing instruments.

It's not totally clear what you mean here. When you talk say the score would "normally play back in B-flat"), do you mean the actual concert pitch key of the music itself happens to be written in Bb? Or do you mean the music is transposed for Bb instruments? And what would it mean to "play it back in E-Flat (without changing the notes on-screen)"? Do you mean you want to hear the music higher or lower, but for some reason want the notes on screen to be incorrect and not reflect what you are actually hear? Like, "what would this piece sound like if it were played on Eb instruments instead of Bb instruments, without changing the pitch"? Do you want to view the notes at concert pitch or as transposed for Bb instruments?

WHatever it is you are trying to do, I'm sure it's possible, but we need more information about your goal here in order to understand and assist better. Ideally, attach your score and describe what you want to be different (eg, "I want to load the score, press Play, and have it sound a perfect fifth lower, or perfect fourth higher, while viewing the score with concert pitch off"?)