I make ginger beer using sucrose, and oddly enough I've tried the same techniques (to attempt to re-start) you have with the same yeast strains, with the same "stick", on a batch a while ago (it stuck at ~1.030), twice.
Twice isn't just a coincidence, so I was especially careful to ensure (1) a full boil, and (2) that no sugar concentrated at the bottom of the boil tun.
Both of these were in an effort to avoid a high concentration of sugar (i.e. syrup) near the heating element. Ultimately caramelised sugar isn't metabolised by either E-1118 or S-05. Same recipe thereafter finished A-OK, so I'm inclined to believe that the caramelisation was the problem.
My money's on your DME having suffered the same fate as my sucrose. You have a full boil already: did you turn off the heat before adding your DME, and mix for five minutes before re-applying heat?
Pretty sure this one is game over, man. I'd chuck it personally, but it's always a hard decision to make...