So what would you say the odds are of fundamental grammatical words and particles changing (leaving the bulk vocabulary alone) versus several large syntactic changes on this order? My armchair understanding is that the later is a lot more likely.
Well some of those changes are not reflected in Scandinavian in general (many Scandinavian dialects have V-to-T, some have V2), so I'm not sure if it's actually relevant to the authors' hypothesis. But some of those changes also happened _in_ Scandinavian in recorded history. So the probability of these changes is relatively high given a 500-year span.
Borrowing "fundamental grammatical words and particles" (I'd go with "functional elements") is common too (the French of Prince Edward Island French is a famous example). That English has Scandinavian functional elements is uncontroversial, and previously was taken as evidence for contact, not descent.
Here's what I see as the facts underlying their claim. English went from a OV, V-to-T-to-C (thereby, V2) language to a VO language with no verb raising, in which it is similar to Scandinavian. I don't see how that's inconsistent with contact.
Thanks for clarifying this for me! I wish there had been a linguistics department at the school I went to, I'm sure I would have minored in it instead of philosophy.