Not a single working solution could be found (short of creating a new Windows user account), nor was a tier 2 Microsoft support rep able to help resolve the issue.
Google and Microsoft having failed me, I was finally forced to stir my stumps.
(Very) long story short, deleting "HKEY_CURRENT_USER\Software\Microsoft\Internet Explorer" restored Outlook Today to its former glory.
Posted to the Microsoft Community for good measure. May the suffering cease!
With a bit more experimenting, I found that simply deleting the OUTLOOK.EXE name value (or changing its value data as explained below) in HKEY_CURRENT_USER\Software\Microsoft\Internet Explorer\Main\FeatureControl\FEATURE_BROWSER_EMULATION restored Outlook Today.
FEATURE_BROWSER_EMULATION "defines the default emulation mode for Internet Explorer". The value data of OUTLOOK.EXE was 2af8, which corresponds to IE 11. Changing it to 22b8 (which corresponds to IE 8) resolved the empty Outlook Today page as well. Here is the list of values from Microsoft for posterity:
UPDATE 2: Microsoft has posted this solution as a KB article: Outlook Today displays no information under section headings
/windows | Sep 11, 2015
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