Cannot install High Sierra or Sierra, get "installer payload failed signature test"
Somewhere along the line it lost its time/date.

If you're still in the OS X Utilities, go to Utilities > Terminal and type

date


to see the current date. Mine was 17 years out of date.
If connected to the internet, update through Apple's server: 

ntpdate -u time.apple.com


if not connected, do it manually

date MMDDHHMMYY


That's month, date, hour, minute, year.
So:

date 1116120717


You can also get to the terminal via CMD+S and Single User Mode, but just do it through the utility.

from these forums I found the incorrect date possibility:
https://forums.developer.apple.com/thread/49094

This site had the steps:
https://www.macworld.com/article/3097533/macs/installing-os-x-what-to-do-when-this-copy-of-the-install-os-x-application-cannot-be-verified.html