In the recent log you posted, 50% frames were lost due to insufficient bandwidth. This is what made your video appear choppy and not 60 fps smooth. OBS produced a stream with bitrate 20000 but your connection to Youtube allowed only about 10000. You said you have 40000 upstream, so it should match, but actually much of this bandwidth isn't available between you and Youtube.
Increasing the bitrate from 20000 to 30000 will not help, because either it is still cut at about 10000 (50% of 20000), or at some other value. What is cut is still missing from the video.
For troubleshooting, don't increase but decrease your bitrate until you get no lost frames due to insufficient bandwidth. The value you get is the bandwidth that is really available for your youtube streaming. It's dependent on the backbone internet connection between your provider and the backbone Youtube is connected to. The general network troubleshooting guide applies: https://obsproject.com/wiki/Dropped-Frames-and-General-Connection-Issues
Yep, that's not the problem. I came to the same conclusion, but further testing cleared everything up. My 1070ti's encoder just isn't fast enough for 4k at 60 fps. I switched over to 264 software and had a completely different experience. Although my i7-8700 fared better, it doesn't cut it either. I actually spoke with a rep at YouTube (shocking, I know) and we tested my bandwidth to google's PoP at generally 37,000 kbps. The reason I was sending less data is because my 1070ti's encoder couldn't keep up. A friend brought over his Zotac GeForce RTX 2080 Ti AMP Extreme and we switched back to NVENC. No dropped frames. 60 fps. no problems. Time to start saving.
Thanks to everyone who responded. I appreciate all of your suggestions!
Just so you know, you don't have to go straight up to a 2080ti. The encoder in there is the exact same as any of the rest of the RTX line, as well as any of the GTX line from the 1650 super and above (NOT the 1650 or the 1650ti -- these use the older Volta encoder). All of these cards should be able to handle 4k60 encoding.
True, but if I'm gonna sling some cash, I should probably do my best to future proof myself. I should be able to recover some cost as the 1070ti is still in demand. It shouldn't be too rough. Thanks for the info, though.