The centre for Quakers on Island was Maughold but that was 1660's to 1680's - after that they dissapeared from view (see http://www.ee.surrey.ac.uk/Contrib/manx/fulltext/rq1908/text.htm) and elsewhere on the site but the anme Moore does not appear amongst their members (Smith is actually a fairly uncommon name on the Island! though Moore is reasonably common). I have done no work on Quaker records but was given to believe that English records of marriages were fairly comprehensive