Hmm, what about some kind of "Brandenburgers" operation (don't have to be the OTL Brandenburgers, maybe another "special" unit from navy and/or Paras and/or combination of all of it) ?
Something like Paras airborne landing on some points at the british coast (not necessarily the "most prominent", maybe somewhere in Kent ? ... Stonehenge ?), supplied by some glider loads (still not very heavy equipment, I know). There they make a lot of noise, blasting something up and ... leave on some sneaked through subs/ E-Boats (at least some of them, there will and should be some corpses left for ... "prove").
Home Guard will boast to have driven the mighty germans away. The germans will counter with a wee smile, that these were only some small scale reconaissance/test missions. However, don't they prove, that germans can, if they would wish, land anywhere, even in Britain ?
Whatever prop the brits may start, I'm sure there will be an "invasion scare". ... Might help to get Halifax around to swallow at least some or one of the toads identified (Iceland, Färöer, Grennland).
... As it seems to me, this ARE the only "toads" there are in the armistice, as outlined by the OP.
Malta, as the only other one debated here, ... well, in another thread (I unfortunatly can't finf in the shortness of time) it was quite well established, that during the war cabinet crisis, Halifax actually considered to giving Malta to Italy, as a "price" for its "good mediation" services.
About as much chance as a chocolate mouse traversing hell.
You do realise the Royal Navy OWNED the channel at night, don't you?