While I don't have either the 930 or 940, I recently changed from the GG&G on my Maverick 88 to a Magpul MAG508. However, that is specifically for Rem 870, and Moss 500/590 (non-A1). It does not mention 930 or 940.

Additional searching lead me to Amazon where I found the Monstrum Accessory Mount Adapter and in the "questions" section it was asked if it would fit a 940 JM Pro and the answer was "It does on mine".

Now, it's set up for a QD sling mount, so I don't know if that works for you or not.