In testing out a couple of mkv files where I altered the flags (to no avail), I have stumbled upon a partial solution, and thought to post for anyone else having the same problem.
I mentioned that there is no menu item to select in order to change the aspect ratio as it is greyed out. But whilst playing around with the test files, I found another menu. Whilst you have a file from your USB device playing, press Tools on the remote control. There you will see Picture Size. Selecting Mode 2 will pull the anamorphic image out to fill the screen as it should be. This only works for 16:9 images though. It doesn't work for other aspect ratios. That is, it will fill the screen, but you don't want that with, say 1.66:1 or 2.35:1 for example.
If you want to watch 4:3 encoded files, you will need to switch this menu back to Mode1.
In playing around, I have also found that this TV doesn't appear to support subtitles in mkv files. Some either play, but with no subtitles, or play with no subtitles, but only for a few seconds, then the image freezes. It is possible to forward a touch, and it will play again, for a few seconds before freezing again.
I have also found that the TV doesn't support chapters in mkv files. I can only presume, without testing this yet, that it likely won't support multiple audio tracks in mkv either.
It's looking like the mkv support for this TV doesn't amount to much support at all, really.