MikTeX 2.9 installs polyglossia in a different location than where it looks for it

MikTeX 2.9 installs polyglossia in a different location than where it
looks for it

I recently did a complete reinstall of Windows 7, installed all updates,
and reinstalled all of my programs, including MikTeX using the 2.9 64-bit
version. I ran a XeLaTeX document I had created and successfully run
before, in order to re-download and autoinstall most of my packages. This
went well, except for polyglossia.sty and gloss-english.ldf, both parts of
the polyglossia package; MikTeX prompts popped up (I had set the
autoinstall on "ask me" at install) twice for the first file and three
times for the second, before moving on and generating the document anyway.
The same thing would happen with those two every time I ran the document;
I tried changing the autoinstall download from "random" to, eventually, a
dozen or so repositories with no better luck. I looked in the directory
cited in the autoinstall prompt, and still no polyglossia directory.
Thinking perhaps it was a glich in the 64-bit version of MikTeX, I
uninstalled it--successfully except that Windows was for some reason
unable to remove the empty MikTeX 2.9 directory from Program Files (86)--I
removed it myself, but had to assert administrator privilege to do so. I
then ran CCleaner on the Windows registry; there were fixes to be made,
but none that appeared to have anything to do with MikTeX. I then
downloaded the 32-bit version and installed it, but everything just went
as before. And I don't even want to think about the manual
download-and-install fiasco that I tried next; it seems you can't get
polyglossia.sty to extract from polyglossia.dtx without polyglossia.sty
installed first.
Then it occurred to me to look in ALL of my C:\Program Files (x86)\MikTeX
2.9\tex subdirectories, not just the xelatex subdirectory where MikTeX was
looking for them, and lo and behold, there polyglossia was... in the latex
subdirectory. For all I know, MikTeX was fetching it and putting it there
every single time I clicked the go-get-it button. So the question becomes:
do I either tell MikTeX where to put it (and how), or where it should be
looking for it, (and again, how)? Or should I just move the polyglossia
directory to C:\Program Files (x86)\MikTeX 2.9\tex\xelatex with a simple
cut-and-paste and be done with it?