It took me 12 days (not months as I previously guessed) but I have an instance of Gentoo installed as a QEMU guest. That includes the time of the initial installation of Gentoo, which went very smoothly due to their superb documentation, the emergence of links the terminal mode web browser, which brought in more than 200 dependencies including the entire X Window System, and a failed attempt to emerge Gnome, which would have brought in another 250 packages but errored out when there are 100 to go. (After the failed Gnome installation, I wanted to clean up a bit and retry. One of the cleanup commands I used is emerge --depclean, which wiped out the 150 packages already installed for Gnome.)
And here's the benchmark result:
On the surface, Gentoo's index of 11.9 compares unfavorably against Ubuntu's 56.0. However, on close inspection, I discovered that the Ubuntu guest's clock is running much slower then the host's clock, which inflated Ubuntu's index.
An rough estimate shows that Ubuntu's clock is running at one quarter of the regular clock speed. So the Ubuntu number should be roughly 14.0, still better than the Gentoo number. Incidentally, with the new lower number, the emulated QEMU system falls into the Pentium 200 category.
So for all that long compile time, I get a Gentoo system that runs at 85% the speed of Ubuntu. Apparently for the system emulated by QEMU, none of the optimizations that I hear Gentoo enthusiasts talking about matters.