I studied Vic Garbarini's article about the recording of Don't Stand So Close To Me '86 and worked on some PoliceWiki pages about that. It looks as if the band started recording on July 21, 1986 and finished mixing it on August 8, 1986. Check out the article linked to on this page and if you have more information about that topic - and about the video shoot ! - then let me know:
http://www.policefans.org/Police_wiki/index.php?title=1986-07-21
Dietmar