I think this is a sure-fire way to achieve this.
I just sent a special offer for 13 days to a guest. But then applied a 'special rule set' to those same days, which I defined as:
* 400% price increase
* 13 day minimum stay period
If you only do the price increase then it's still possible that someone would make a booking where only one day overlaps with your special offer date range, and then the total may still be acceptable to the guest and book it. (e.g. 7 days at a regular $75 and 1 day that was part of your price increase at $400 for a total of $925 for an 8 day stay which may very well still be an acceptable price to the other guest.
But to require a 13 day period at a really high price makes it exceptionally unlikely to get booked by someone else, and you don't need to disable instant book for all other dates.