I would recommend against disciplining the employee for his behavior thus far. The managers granted all the meetings that the employee requested. Retroactively punishing him for these agreed-to meetings would send a very mixed message and be perceived as grossly unfair.
Assuming the employee has had all of his questions answered clearly, in a way that he should be able to understand, I would suggest telling him that the topic is now closed for discussion and additional working time should not be spent on it. This conversation (or e-mail) should not come across as discipline or even a warning to the employee, but you should document it in case the situation escalates further.
The employee's classification is squarely within his "terms and conditions of employment," and discussing those terms and conditions is the right of all employees protected by the National Labor Relations Act. As result, you can't stop him from—or punish him for—talking about this issue during lunches, breaks, or outside of work, but you can certainly not grant him any additional meetings and you can request that he stay on task during his regular working hours.