I am unfortunately completely ignorant of how you actually send data to Twitch, but can you use H264? It has an "ultra-low latency" mode.
Edit: Hmm, you're on OBS. Maybe you could stream using some uncompressed low-latency option from OBS to ffserver, then reencode on ffserver to low-latency H264. Alternatively, you could use ffmpeg with its X11 capture option, pointed at eg Xvfb.
I am unfortunately completely ignorant of how you actually send data to Twitch, but can you use H264? It has an "ultra-low latency" mode.
Edit: Hmm, you're on OBS. Maybe you could stream using some uncompressed low-latency option from OBS to ffserver, then reencode on ffserver to low-latency H264. Alternatively, you could use ffmpeg with its X11 capture option, pointed at eg Xvfb.