Thanks for the feedback, dave_van_damn. I have now succeed on getting the game running on Dreamcast (the specific file IVAN GR posted by in August).
However, I noticed that the most recent version posted on Gamevolt has some October updates, including playable Casey Jones and April O'Neil:
https://gamejolt.com/games/TMNT-The-Hyp ... XED/361489
I haven't yet been able to get this version running on Dreamcast, as it loops at the "produced under license" screen. The file size looks to be about 770 MB, which seems like it should be too big for a standard CD-R. Anybody know what I might be doing wrong trying to burn and play the most recent option?