This is the reason I am returning the hd60. You cant just use the elgato as a video source for streaming. You have to use their software which looks pretty, and is simple for newbs to get started capturing, but is the biggest processor hog I have ever seen. Then you want to run something on top of that to capture the window (that keeps resetting if you click away from it) and you are approaching the need for a Cray.
As a comparison, I stream flight sims (big-time resource hogs) directly from my mac using OBS Studio and I used to get alot of compliments on my stream. I wanted to add some 360 games so I tried the hd60. Fail.
As a fellow mac user, your choices are to either install a copy of windows using bootcamp to use the hd60 as a streaming device (not fully supported in OBS), or return the hd60 and wait for an HDMI to thunderbolt or usb3 cable solution (don't hold your breath). The hd60 being usb2 instead of usb3 is quite frankly, a gigantic fail from a streaming product perspective. I hear it captures just fine for editing if that is your thing. Apple also takes blame for ditching firewire after there were tons of video gizmos on the market.
Someone told me that getting a copy of the TV3 software from elgato as a custom request also solves it, but I dont think I will wait for that. I'll just return the hd60 and try something else.