teabag do you have a link please? Have looked at owners direct/holiday lettings/etc and as you say most want 7 nights. Must be something somewhere. Budget around £700 max for 3 nights, dates 25/26/27th Oct or mid week break from the 28th.
have a look at bigholidayhouse.com and groupaccommodation.com websites both are really good. lots of places now only taking a week booking for Oct half term so might need to go for say the end of it and go for place with a Friday changing day.