BSP,
as you will be well aware, I am something of a stickler for CCers doing just that, and regard the "as is reasonable in the circumstances" fairly narrowly, to encompass unforseen personal circumstances and short notice stoppages.
I have never regarded "well I need to be in an area for 4 weeks for something predictable" or " well there is a planned stoppage that I've contrived to be blocked by" as fitting the bill.
However, in this case I find myself unexpectedly on the side of the doves, with other forum members distinctly more hawkish.
Provided you can honestly say that you moved onto the summit without being aware of the impending closure, and provided you could not easily have left the summit between the closure being announced and it being implemented, you are currently trapped through no fault of your own.
BW are within their rights to say "well you must move on or pay", but NOT to impose such a restrictive time window.
I would suggest that you respond explaining that you are not able to move on that date, and that you do not wish to remain there. You should then explain that in the absence of this stoppage, you would have continued your journey on [DATE], and again on [DATE], listing all the dates on which you are able to move between now and March, and offering to move off the summit level on any of these dates if they will facilitate it, but making it clear that whilst you are fully able to maintain a cruising pattern that involves moving at least once a fortnight, and have agreed to do so, you are not able to move at a few days notice, and that if you are unable to move as expected on a particular day, you are not able simply to move on the next day.
NABO would probably help if you are a member. If you would like me to help with drafting a letter, let me know (and you DON'T have to join my fan club).