I know you're getting hold of the war diary, which will help.
Have you checked out the Photo Gallery, there are a few photo's, it looks like the sources are all regulars here so I'm sure someone will be along shortly.
I have got the contact details for a veteran who was an American volunteer with No6, Gaylord McCurdy or as he is generally known Mac. I could send him a message asking if it would be ok for you to contact him concerning No6's involvement in the N.African campaign. My father was also there, but with No1 Commando who also had American volunteers, all the Commandos from No1 who took part in this received a certificate of thanks. However I have been told that No. 6 were also issued with these cerificates, although I have not yet come across an example of another one either from No1 or indeed No6, my father's certificate can be viewed in the gallery.
As you are probably already aware both No1 and No6 were issued with American equipment ie helmets and weapons, particulalrly the Garrand semi automamtic rifles. When I recently met a veteran of No1 Idris Jones, he told me that they were initially asked to wear an American flag under their existing insignia, which at that time was the 1st pattern shoulder title and the Salamander in flames. However they refused and the order was withdrawn, there is a nice example of an original salamander and 1st pattern shoulder title in the gallery, that was worn throughout the Tunisian campaign by American No1 volunteer Maurice Jones.