At the time of me writing this, all NVIDIA GPUs in a generation have the same NVENC chip (RTX 2060 = 2070 = 2080 = 2080ti). Have a look at this NVENC Matrix from NVIDIA:well I have kept researching it and even though my recordings have smoothed out and work now without the game mode on it still confuses me......
An RTX 2080 will be overkill if you are only using the 2nd PC for streaming/recording. If you are determined to get an RTX 2080, then I would use that as your main driver and put your 1080ti in your 2nd build for dedicated streaming. You would also need a capture card (EposVox on YouTube will be an excellent resource for you to decide which capture card you want).
Alternatively, if you want to install a second GPU in your current build, YouTuber Battle(non)sense has done extensive testing into what you can expect to see when dedicating a second GPU to NVENC:
Also, I tried SLOBS last night, and my frame rates were back to normal again (even when I had dozens of chrome tabs open, researching what could be going wrong with my setup). Does anybody have any insight as to why SLOBS would be performing better than OBS (settings were imported directly from OBS)?