Lolz that is just silly, these Pascal chips are so damn lazy.
Nvidia made them way to power efficient as they just cut power once they find a second of lesser load, i saw/see it on my 1070 FTW('s) both Samsung and Micron memory chips, both felt the same, so not much of a difference, but then again EVGA send the new 1070 FTW to me with an updated BIOS on the new Micron card and i push more memory overclock on the micron chips than i did on the Samsung.
But i never tried running anything on 1080p, as i got the 2560x1440p Dell screen which i overclocked to 65 Hz as i saw V-sync messed up a few times on the regular 59-60 Hz it is on default.
Only game that gives me any grif is The Crew, as it is so light to run on a 1070 then it some times run it with default clock speeds which results in some minor lag spites a few times.
But i think i'll never have your power delivery issues as my EVGA card have a overkill 2x 8pin and 8+2 phases of VRM's, but then again i was dealing with heat issues and now you got power delivery issues.
Pascal seemed great, but Nvidia had to mess it up. Hopefully AMD can knock in a few teeth's on Nvidia as Nvidia needs a wake up call badly, as they seem to think they can do what they want - even spy on they GameExperience users YUP they collect game data on your PC, but i honestly don't give a damn if they do it or not, only think they'll find is a few dirty links as everything else of importance is backed up in the cloud.
BTW less power uses normally means lees heat so that should be a win for your compact case.