Finally figured it out!
Thank for leading me down the right path @Dist.
For posterity:
Use the new Helix API instead. Request a token with the code. (Docs link from @BarryCarlyon below) Then use that to get the user’s ID/username. And finally with API v5 make a call to the channel you’re requesting for the basic info.
https://id.twitch.tv/oauth2/authorize?response_type=code&client_id=<CLIENT ID>&redirect_uri=<REDIRECT>&scope=<SCOPE>