I'm positive that direct output/playback cards are still very much a thing for Premiere/AE. I can't say I have direct knowledge of them and I'd also guess that many of them are set up for processing RED footage, but I'd be amazed if you couldn't find something that fit your needs.
Actually now that I think about it, in our client room at work we do a direct output of the AE comp window to a TV monitor via HDMI. I'll look into it.
EDIT: Confirmed. We're using the Black Magic Intensity Pro (internal card) http://www.blackmagicdesign.com/product ... ty/models/