First, I tried the standalone updater. The package installer gave me an error with a giant yellow caution sign. It said, "The installation failed. Could not prepare Security Update 2018-001 for installation. Try installing from a different copy of the item or contact the manufacturer for assistance." I called Apple and they were very sorry this happened. Tim's going to get back to me later today with a fix. Actually, to be accurate, Apple doesn't care about me. I made up the part about calling Apple. The error message is totally, 100% real, though.
In past updates, the App Store update wouldn't work, but the standalone updater would work or vice versa. I figured, "OK, this is one of those times when the standalone updater doesn't work but (fingers crossed) the App Store update will work."
So I tried the App Store update. I got a little bit further with this. After it finished downloading, there was a message about restarting. So far so good. Pressed restart. The screen turned black and there was a progress bar. After a bit it (the progress bar) said "Restarting." The progress bar went away and there was a momentary gray spinner. Then the first reboot. Alas, in Clover, I didn't get the "Install Mac OS from ..." boot option.
Although I believe I am the only person in the world with this issue, I'm just going to kind of follow-up here, so there's some sort of record.
I managed to get the update (17E202) installed just now. As I stated before, the updater wants to use my recovery partition for it's intermediate, reboot-and-install stage. When I had tried the stand alone updater Clover didn't present that boot option (the update didn't work). After that I tried the App Store updater and it also didn't work.
This morning it occurred to me that perhaps the stand alone updater (performed first) had left a mess behind that kept the App Store updater from working. I mounted my recovery partition, and sure enough, there were two extra, non-recovery related folders in there. I removed them and tried the App Store updater again. It worked.
I recently made this update, and now my bluetooth is wonky. The chip on my Asus GA-H77N-WIFI is still recognized, but it bluetooth cannot be turned off, and now my Apple trackpad and keyboard will no longer pair. Anyone have similar issues or have any recommendations?