Your statement ("modern executive interpretations that 'due process' in the law simply means any established process") is not consistent with Holder's statement, as described by the very title of the article you linked to: ("Attorney General Holder: Due Process Doesn't Necessarily Mean a Courtroom.")

Due Process does not require a courtroom. That does not mean that "any established process" will suffice. The amount of process due depends on the context. The open-endedness of the concept is embedded in the phrase itself: the word "due" means "warranted" or "appropriate."

I don't think there's a Supreme Court case specifically involving police officers, but the general idea that public employees have protections against suspension is well-established: http://www.huizenga.nova.edu/course-materials/6240/cases/Con....

You are correct that a balancing test is always going to be more vague and open-ended than hard, bright line rules. But the advantage is that it lets the courts adapt to new situations flexibly. This is the entire approach of the "common law" on which our legal system is based. And when you are familiar with prior court cases in which judges have applied the test, the test becomes less vague and open-ended.

For example, there are seminal court cases that lawyers know in which 1) a person has their welfare benefits revoked, 2) a person has their disability benefits revoked, 3) a tenured public university professor is fired, and by knowing those cases, you gain an understanding how most courts would likely view the suspension of pay of an officer with no notice or hearing of any kind. Different facts will obviously change the results, and different courts may come to different conclusions, but the current test and existing case law is not impossibly vague or unworkable.