I successfully installed High Sierra! After installing Sierra, I went to the App Store to download the High Sierra, expecting it to be the 19MB pseudo installer. Lo and behold, it downloaded the full 5.2GB installer! I decided to try Unibeast again to make a USB installer with the full-sized installer app downloaded through the App Store and it showed up in Clover! And yes, it installed 10.13.2. (the rest is copied from my post on my own thread trying to figure out this issue).
Install went fine (well, except for the fact that I left all of my drives plugged in and every time it restarted I was out of the room so it booted into El Capitan. Then I had to restart and had to keep choosing something like "Boot from macOS on Install macOS" on an internal drive, and eventually that changed to "Boot from macOS on High Sierra" once the install completed). Now I'm having trouble getting High Sierra to boot from Clover on the EFI partition on the High Sierra internal drive. I suspect I'm missing a kext or something in the EFI partition. I assumed after running Multibeast I'd be able to boot without booting Clover from the USB, but that hasn't worked yet. That's a separate issue however.
For me at least, I can confirm that the Unibeast created USB installer using the full-sized Install High Sierra app downloaded through the App Store does work. So my previous assumptions were wrong apparently. The issue does not lie with Unibeast or Clover, but with using dosdude1's patcher utility to download the installer. I would suggest first installing Sierra, and then seeing if you can get the full installer from the App Store in Sierra. I never could get the full installer in El Capitan.