My insane solution...
This covers both "no monitor wake after sleep" and "no monitor display on cold boot."
1) Plug LG 4K monitor (HDMI 1.2) into old Apple USB-C to three ports (only one of which works at a time). Don't use that connection, because the resolutions available are limited and higher resolutions look bad.
2) Plug cheap, standard USB-C to DisplayPort cable into monitor and computer. Use this for the actual display by setting monitor to use the DisplayPort connection.
3) Keep second (HD) monitor on Mac's HDMI output.
I don't know why this combination works, but it does. It actually would work with Apple's display adapter, too, but that isn't really usable (visually). The Apple display adapter seems to calm the Mini 8,1 when it boots, and gets it all friendly, so it talks to the monitor via DisplayPort and the old HD monitor via HDMI.
Plugging the main monitor into the HDMI port results in "no wake on cold boot." Plugging the Sceptre (HD) into HDMI results in "no wake on cold boot." This combo works. I don't know why but all it costs is a useless adapter I paid too much for and never could use (it's rated all of one star on Apple's own store) and one USB-C port I wasn't using anyway.
I now have every single hole in the Mac Mini 8,1 filled, which is fun but might be a pain someday.... what's with the crazy high cost of USB-C to USB-C cables, anyway?