Yep, fast-motion games and 1080p don't mix well, unless you're Twitch partnered and have the transcoding options available. Even MOBAs kind of line-ride, much less FPS games.
Either you'll be pushing BIG bitrates to keep it looking good (causing viewers on mid-low connections to see lag, stutter, and other poor stream performance), going with lower rates causing a drop in image fidelity (as it seems you're doing now), or dropping your framerate to save some bitrate by pushing fewer frames over the same band (making it look less fluid).
I'd recommend waiting until your new connection is in, then run the 6MB test at
http://testmy.net/upload to determine your actual stable throughput (speedtest tests for dead-file transfers, which are unaffected by 'bursting', spiking and dropping rates that average out over time; gaming and livestreaming require a stable minimum throughput available at ALL times) and work from there; don't forget to leave some for your game as well.
1080p@30fps, I'd shoot for 3000kbps minimum for a passable image quality. 3500 would be better. Depends on what your new connection actually has, real-world.
It'd almost be better to downscale to 720p and jump to 60fps (if you have a beefy enough CPU to handle the extra encoding); it won't look /as/ good in fullscreen, but the motion will be MUCH smoother, and a more pleasant stream to watch.
