00:17:30.205: psycho_aq: true
Try turning off this feature. It's called Psycho Active Tuning. It uses a small amount of GPU.
00:16:35.025: base resolution: 1366x768
00:16:35.025: output resolution: 1920x1080
Lowering your base resolution and then upscaling your output resolution would reduce rendering lag, but it would not reduce encoding lag; in fact, compared to not scaling and just using 1366x768 as both canvas and output, would create more encoding load.
That said.. I do not see why your machine should not be able to do 1080p60 under normal conditions.
Have you checked that drivers are up to date, and that the card is fully seated in the correct slot, and is getting the maximum possible PCI bandwidth?