I guess the easier question would be, how can I get the trumpet to agree with every other instrument's transposition?

Changing key signature will (by default) transpose your music up unless you change the defaults.

(Now you've changed the question.)

To get the trumpet where you want it, select the measures in the trumpet staff that need transposing and use the Utilities > Transpose function to put it where you want it. Be sure to confirm whether you are seeing the score in concert pitch or with transposing instruments transposed (in the Document menu) before you do the trumpet transposition.

That is how I set up the trumpet transposition, using Utilities > Transpose; the part switches between the two instruments fairly frequently. All of the other pitches were entered after the key change was made in the score. Score is set up as transposing, not concert pitch.

I've been having some other strange playback problems today. I tried just restarting the software entirely, which fixed it for a while. It seems that there may be something entirely different going on.