I don't think Plusnet take account of other ISPs Ts&Cs but it could be a happy coincidence. That is better than the default 30 days.
As far as switch date the 8/10 is a Saturday and therefore not a day that BT do customer migrations - I believe they are only available on weekdays hence your issue.
PS - if you cancel your contract with PlusNet then it could leave you with weeks of downtime - reconnecting after a cancellation can be very time consuming. Your best move will be to do the move on 10/10 and pay for 2 or 3 days at the new rate.
Edited by ian72 (Thu 15-Sep-16 16:32:47)