This issue went away by removing Compatibility View.
Specifically, I have the CMS in Local Intranet Zone per the documentation (which also solved Blocked CSS files for Session Preview only in Internet ExplorerBlocked CSS files for Session Preview only in Internet Explorer). In this case, I had to uncheck "Display intranet sites in Compatibility View" Tools > Compatibility View Settings, close the component and try again.
Using IE's developer tools (F12) reminded me the setting was wrong. You'll see something like:
HTML1201: cms-domain is a website you've added to Compatibility View.
HTML1202: http://cms-domain/WebUI/item.aspx?tcm=16 is running in Compatibility View because 'Display intranet sites in Compatibility View' is checked.