Is it ethical to refuse enrollment of a previously dishonest student if you are the sole instructor for a required course?

It's not up to you

It's reasonable for an instructor and syllabus to specify what happens in that course in certain circumstances. However, going beyond your particular course (including future semesters of it), any further academic punishments for plagiarism or cheating, including being restricted from taking or retaking certain courses, are up to the wider department, faculty, study program, or however your institution organizes things. There should be a universal (not made by and for a single course and instructor) policy on what are the wider consequences for certain acts of plagiarism. Perhaps that policy prescribes that being forbidden to retake that course (or some time limit) is an appropriate punishment, in which case your actions are valid. But if it does not prescribe that students will be prevented from taking future courses, then it's not up to the course syllabus or the instructor to unilaterally decide whether the student is eligible or not.

Note that I'm not saying that you should waive the policy just because it disrupts the path to graduation - there certainly can be academic dishonesty policies that may prevent students from graduating in case of plagiarism. But the question does not mention any specific wider policies, and if it eventually does come to a ad-hoc decision regarding a particular student, that still would not be your decision to make, this should be escalated to your superiors.

Maybe it’s worth remembering that “your class” is not actually “your” class. It is a university class that you were assigned to teach, and it is your job to teach it to whoever the university decided is authorized to enroll in it.

Professors sometimes have discretion to let people into a class when they lack some of the formal prerequisites. But there isn’t a university on Earth where a professor has blanket authority to prevent a student in good standing (assuming they have the formal prerequisites) from taking “their” class. A university could not function if it allowed professors such freedom.

I have strict policy on my syllabus that states plagiarism will result in failing the course, a judicial review incident report, and refusing to accept them as part of future cohorts.

This policy is not enforceable. You are overstepping your authority.

Personally I do not want the student in my class again.

We all have things that we “personally do not want”. That is completely reasonable. But having a job means you sometimes have to do things that you don’t want to.

Should I just grit my teeth ...

Probably. That is a good way to vent frustration about something you’re unhappy about.

... and waive this policy ...

Since the policy is not enforceable, it is meaningless to ask whether you should waive it. You not only should let the student into the class; you simply have no choice in the matter.

Is it ethical to refuse enrollment of a previously dishonest student if you are the sole instructor for a required course?

The ethics question is a red herring. Since you’re not allowed to refuse the student’s enrollment, it is meaningless to ask whether such an action is ethical.

To not allow a student to take a course (specially if it is a required course) is the same as not allowing to graduate. And that is definitely a decision reserved for higher powers, as it is the same as expulsion.