Would I be eligible for the ISA allowance for the current tax year if I cancel my Cash ISA after the ISA deadline (i.e. in the next tax year) but within OakNorth’s cooling off period?

No. For example, If you open a Cash ISA on 28^th March 2020 and cancel the ISA account within the cooling off period of 14 days (i.e. after 5^th April 2020 but before 12^th April 2020) then you will not be eligible for the £20,000 allowance for the year 2019-2020 tax year.