I have got one of the problem websites to work by adding the reg entry
myching.exe=Ox2AF8
@ HKEY_LOCAL_MACHINE\SOFTWARE\Microsoft\Internet Explorer\MAIN\FeatureControl\FEATURE_BROWSER_EMULATION

However this website is still giving problems
http://www.onlineclarity.co.uk/friends/hexresults.php?nr=27
(See attached error dialog )

Trying myching.exe=Ox2AF9 doesn't work either.

The diagnostic website www.whatismybrowser.com, would seem to confirm that it is not running in compatiblity mode with these reg values.