After a bit more research, you can tell the embedded Webcontrol to behave as IE9 rather than IE7 by creating this registry setting:
[HKEY_LOCAL_MACHINE\SOFTWARE\Wow6432Node\Microsoft\Internet Explorer\MAIN\FeatureControl\FEATURE_BROWSER_EMULATION]
"ehExtHost32.exe"=dword:00002328
That's for Win64. For Win32, it should be (untested):
[HKEY_LOCAL_MACHINE\SOFTWARE\Microsoft\Internet Explorer\MAIN\FeatureControl\FEATURE_BROWSER_EMULATION]
"ehExtHost.exe"=dword:00002328
More info at http://msdn.microsoft.com/en-us/library/ee330730(v=vs.85).aspx
(0x2328 is 9000 in decimal; the default value for apps using the embedded webcontrol is 7000 which means ehExtHost.exe normally an IE7 version of the WebControl).
Unfortunately, even after adding this setting and confirming that MCE webpages now report IE9 rather than IE7, it still doesn't seem to fix the compatibility issues with Leanback; for example, the remote control arrow keys work fine in Leanback on the desktop but are ignored in Leanback running inside MCE.
Eddy