If your understanding of the orthodox view is correct (and since you claim some personal expertise in this area, I presume it must be) viz
My understanding of the orthodox view is that prolonged close contact between the West Germanic Anglo-Saxons in the south and the Scandinavians in the north led to the development of a Germanic lingua franca which after a few generations developed into a full blown Germanic based language, English.
Then all I can say is that Orthodoxy is slightly pottier than I had previously given it credit for.
The orthooxy I had been attacking (as a "strawman") was that English is an evolved form of Anglo-Saxon. Since, as you say, "languages naturally change slowly over time" and getting from Anglo-Saxon to English in the time available is nigh on impossible, I am not surprised to hear that cutting edge research is now postulating the insertion of a pidgin because, as you say, pidgins by definition change quite rapidly.
I apologise for attacking the previous i.e. strawman orthodoxy. I was relying on the standard text books taught at the present time to all relevant undergraduates (for instance, English Literature students). This is very remiss of me and I will be circulating your strictures to the many thousands of academic institutions still teaching these now-exploded notions.
However, I feel duty bound--since it is new to me--to explore the way this pidgin (or lingua franca as you somewhat confusingly call it, the two things being rather different). Never mind, let's see how it arose. I think it is the orthodox view that everyone south of the Danelaw spoke Anglo-Saxon. You say that these people felt a need to develop a lingua franca with the Danes then foming a ruling caste in the Danelaw.
Why would this be...to pay the Danegeld...to book tickets on the Stavanger ferry...er...perhaps you'd better tell us, you being an expert in this particular area. No better still, you'd better tell all the people writing in Anglo-Saxon right up till long after the end of the Danelaw. "Hey chaps, why are you still writing in Anglo-Saxon? We're all talking West Saxon-Danish pidgin out here."
It's a shame the scribes didn't listen because by another of those amazing flukes of unwritten history, this pidgin didn't get written down. Nor, and this is even more unlucky, did anyone feel like mentioning this language. Imagine that, everybody's speaking a brand new lingua franca and nobody noticed! [Anglo-Saxon Chronicle Year 995 AD. New pidgin has reached Isle of Ely; memo to self: erase this entry next year.]