A friend told me that he found an Agri-Castrol product called "Self-levelling grease", aka "Pourable grease", which, used in vintage-type boxes like the Burman and Sturmey Archer, (and the worm drive rear axles of Thornycroft cars which leak when SAE 180 is used ), does not leak out. He describes it as a miracle, instant cure. (It avoids the problem of grease thinned with oil, in which the grease and oil do NOT mix, and the oil leaks out.) It has become his "vintage gearbox lubricant of choice". It might not be easy to get in small quantities, but since any farm with a grass cutter will use it in the gearboxes on the cutting discs, doubtless charm and obsequiousness will work as they often do. OK, there's another obstacle, which is that it isn't VERY pourable, and might have to be warmed up to get it into the box.
He also mentioned that farm suppliers hold lubricants in viscosities Halfords don't know exist, like SAE 240, which is potentially useful to know. They probably also stock fling-resistant chain-saw oil, which I know works perfectly in Scottoilers, but is only 1/10 the price of Scottoil.