I downloaded and extracted the intel skylake (https://www.funtoo.org/Intel64-skylake) stage 3 tarball onto a machine with an Intel Celeron G3930, and attempted to chroot into the new installation. However, it reports, "Illegal instruction", every time I attempt.

I may attempt the other tarballs in that series, just to see if there's a difference, but I don't need what they offer as this machine will be headless. I may also run the generic x86_64 tarball if all else fails.