Also sorry you didn't get any replies.
Yes, it should work just fine in the Mark III. I can't quite tell how large the board is from the pictures on the Curcio site, but it looks like it will fit. You will have to change the cathode current measuring resistor values on the output tubes to make it work. Keep in mind the board has the capability to control 4 tubes so two of the outputs will not be used in the Mark III. I see no other reason why it won't work. Caveat - I did not examine it in deep detail. I can do that if needed. So can several of the other guys here.
BTW - there are simpler ways to maintain constant current through the tubes. See this thread:
http://www.diytube.com/phpBB2/viewtopic.php?t=2480
Mike came up with a great way to do that with a three terminal regulator.
Hope this helps. Let us know if you need more info.
Regards,