More detailed, but I think there's some records/debates concerning the Constitution [and its ratification?] dealing w/ Judicial Review: essentially it was considered but rejected. {Strict Constitutionalism doesn't allow it... of course many 'conservatives' would balk at strict Constitutionalism.}
It wasn’t judicial review that was considered and rejected. I think you’re thinking of judicial veto. That’s different, as you can veto whatever law you want for any reason, whereas review only allows you to strike down laws that conflict with higher law.
As for strict construction, admittedly “judicial review” is not mentioned in the Constitution at all, and surely not specified under “due process.” However, nothing is specified under due process. To understand what they meant we must seek how they understood the term when amendments 5 and 14 were ratified. I haven’t done such research myself, or at least not extensively, but have been led to believe judicial review was among the processes due to whomever is owed due process.