P-Channel MOSFET to delay full power
Vgsth is too variable from part to part, and the response of the FET to soft to the gate voltage around Vgsth, that you should split your circuit into a sense part, and a power part.
Use a proper comparator in the sense part.
Use a power FET in the powe part, that gets switched by the comparator.
More complicated I know, but you can make it work to your specifications.