problem with random key changes

[dflat]

As far Green Dolphin St., that's amazing to hear, I've been playing that song in C maj for 30 years, as have other folks I've played w/. C maj is the key it's in in the original Real Book, the "illegal" one from Berklee.

True, the one in that original Real book is in C. In the updated legal versions published by Hal Leonard, Volume IV has it in Eb. Also Eb in the New Real book series (Sher music) (volume 3).
Like you, I usually play it in C although some horn players call it in Eb.

I must be hitting the Song Transpose key somehow by mistake as I'm playing around w/tempo, rhythm styles, etc. Sorry.

It might have imported set in F# (default key) but shown initially in A. This is normal if the song was set to A in song view (it remembers).
Or you could have inadvertently changed it in song view as you say. There is a fast mode where you can tap on the key (or repeats, tempo) and drag up to change the value. (This is explained in the Tutorial>Player). You probably did not do this without knowing you were doing it, but it could have been possible also.