Twitch doesn't allow a variable bitrate, which would really help here. But you can set your framerate lower with a corresponding decrease in bitrate. For example, a typical recommendation is 2000 bitrate with a 2000 buffer at 1280x720 by 30 fps (or 2000/2000 720p30 in the common shorthand). You could easily set the framerate to 10 fps and lower the bitrate by 1/3rd. You could stream at 1080p and lower the bitrate by half using 10fps and when things move, it might block a little at first, but it will clear up in a fraction of a second.
I'd try 1000 bitrate, 1500 buffer, 1920x1080, 10fps. Normally we recommend keeping the buffer equal to the bitrate, but I think in this case you want to increase it but keep the nominal bitrate low.
If your native screen resolution is larger than 1920x1080, use a downscale to make it as close to but to not exceed 1080p.
At these low settings you can probably increase your preset as well, Going to Faster or Fast instead of Very Fast, for example. And naturally you should experiment to dial in the best settings possible rather than continually use my best guesses.
Edit: I see you said you want to decrease your encoding, not increase it. In that case leave the preset alone, encoding 1/3rd the frames will make the encoding process a bit more than 1/3rd as intensive on your CPU (diminishing returns doesn't give you the full 1/3rd). You can also try using SuperFast preset to decrease the CPU usage further, or try Quicksync or NVEnc encoding, if you have the right CPU/GPU.
