I just installed an EVGA 560TI 1GB card in my X51 R2 with a 330W PSU playing PUBG and it was running for hours full speed and didn't flinch. The EVGA 560TI is a 210W TDP card so it should have no problem running the GTX 10 series cards... unless you got a bum PSU.
I strictly recommend running blower style coolers though, the EVGA got quite hot because its fan over open heat sinks, anyhow it still worked with no problems. Hope this helps.
Well, actually the information I just posted above might be incorrect. I checked another source and the EVGA 560ti is said to have a TDP of 170W, not 210W. Also, my X51 has the 330W PSU, i7 4790, 8gb RAM, Samsung SSD, and a noctua 80mm exhaust fan mod and it will not boot with a GTX1080 installed. So, if it works with the 170W GPU I will be forced to add a higher Watt PSU or downgrade to the GTX1070.