I had the same/similar problem which I've sort of resolved:
To get the ringing tone for incoming calls, I had to set 'play sound for notifications; to on (under profile picture//settings///notifications) - this mean syou get all the annoying pings everytime someone messages you BUT, you can turn these off for channels within specific teams (one by one) although apparently not on any chat threads. Kind of annoying that they don't let you distinguish between incoming calls and new messages - another one for the wish list.
cheers