@briancurliss can't comment on GH+Zendesk integration but Aircall is designed for small teams, that generally not only do phone support. Feel free to have a free test drive on aircall.io to see if you like it.
Hey there!
We're releasing today a new way to handle calls into Zendesk. A smooth, easy-to-use and beautiful phone right into your preferred helpdesk software. Looking forward to your feedback!