PSU - test with a multimeter:
https://www.lifewire.com/how-to-manually-test-a-power-supply-with-a-multimeter-2626158
Not a full test per se as the PSU is not under load.
600-650
"And I'm pretty sure the recommended 600-650 is for an entire system including a 1080 ti maybe?"
"Maybe" being the operative word.
By specifying a PSU wattage (e.g., 600 watts) the GPU is pretty free to be whatever wattage it happens to need without being pinned to some specific wattage value or some "low to high" wattage range. Worked for awhile when GPUs were not as power hungry and tended to demand less of a PSU. Both in terms of wattage or some % thereof.
As for wattages what PSUs can provide and what components require are often established under ideal circumstances.
So if the PSU is "over-rated" and the various components likely "under-rated" the difference between the two values is likely to be actually less than expected.
Then if the PSU is older, lower quality, defective then there is a narrower margin. That is all the more reason to take a closer look at quantifying the wattages.
As for some % spike, GPU or otherwise, the event may happen and crash the system faster than the event gets processed and visible in the graphs.
Reliability History and Event Viewer may capture and record some pre-requisite event so you end up interpreting the chain of events....
Overall I would not be surprised if the GPU is okay with supporting one monitor but the demand to support two monitors may be more than the system/PSU is able to handle.
Do you have a Kill A Watt type meter? If so you can put the meter between your computer and the wall outlet. Then measure the wattages while system is idling, while doing light work with one monitor, two monitors, and then gaming: again one monitor, two monitors.
The results may be revealing.