OK, we went with Ingrid Flute - they had a cancellation. So, we've booked a 4-person cottage next to the Magpie (double room for us, twin for somebody else, dunno who yet). Problem solved; thanks everybody.

(It occurred to me that the real problem with Whitby is that it doesn't have a residential college; most towns of that size do, and they add a lot of elasticity when trying to fit people in for major events during the college holiday period).