After a little more searching via Google I now finally realise that the crude reproduction published by Fremont-Barnes is actually of the painting discussed by Robinson, and illustrated by him in B&W; on page 235. I have not discovered where the painting is now. It is however available in (variable) colour on at least two internet sites; Here:
http://territorialmasquerades.net/wp-content/uploads/2011/09/Barbary-Pirates.jpg
and here:
http://gatesofvienna.net/2010/12/a-19th-century-jihad-on-american-shipping/

What is odd is that Fremont-Barnes has reversed the sense in his reproduction, which confused me for a while.
On page 235 Robinson states that he has "little doubt that this is the version Kirkall used". Kirkall's mezzotint is in the reverse sense of the original. It is perfectly obvious that although this original may not have been painted by the Younger van de Velde, and certainly not by the Elder, it was equally certainly not painted by Peter Monamy.

This is a very disagreeable and unpleasant discussion. I realise that your inadequate research is being exposed, and I'm sorry it upsets you.  I recommend that you take a good look at Robinson's opus. He is far more reliable than the sources you quote, and that includes Callender, who perpetrated a number of incredible howlers in his writings.