I've fixed it!
My problem was as simple as the "P" in "Precise" in /etc/lsb-release under "DISTRIB_CODENAME" being capitalized instead of lowercase. It should be:
Code:
DISTRIB_ID=Ubuntu
DISTRIB_RELEASE=12.04
DISTRIB_CODENAME=precise
DISTRIB_DESCRIPTION="Ubuntu 12.04"
Other files of note:
/etc/issue:
/etc/issue.net
As mentioned previously, it seems that one needs to both enable the partner repository and add the lines mentioned to /usr/share/software-center/softwarecenter/backend/channel.py (or uncomment them if they're already present).
Thanks for your input, everyone! I can't believe it was such a silly mistake... ;-D
--Dane