You could cross Powhillon if you get the current tenant farmers permission. Problem is once you get out to Powhillon's merse you are in an SPA/SAC that was designated for Barnacle geese and if you disturb them the WWT can and have done in the past, prosecuted those caught shooting.
SPA designation: http://www.jncc.gov.uk/default.aspx?page=1980
The whole secrecy thing around that part of the Solway is because the BASC and Solway Wildfowlers Association have an agreement with WWT to restrict and not promote wildfowling in the area.
SWA and BASC agreement: http://www.powhillonfarm.c