In general you should always use multiple constituency tests, because some are too general and others too specific. In this case, we can also use coordination (The angry boss and the mean supervisor fired me), clefting (It is the angry boss who fired me), pseudoclefting (The angry boss is who fired me), passivization (I was fired by the angry boss), and answer fragments (Who fired you? — The angry boss), probably among others.
The replacement test is best done with proforms: pronouns or empty verbs like do so/it. This is called proform substitution. We cannot easily replace angry boss with a pronoun, because of the definite article The. What you are doing is general subtitution; the linked Wikipedia page gives various examples in which this test fails.
The proform substitution test is more reliable, and fails with slowly ate. This test can be used to show that slowly ate a donut is a constituent ((John slowly ate a donut, and) she did so too), but this fails with slowly ate (*John slowly ate a donut, and she did so a bagel).
There are other tests that you can apply as well. For example, answer fragments: you can have What did she do? — Slowly eat a donut but not *What did she do a donut? — Slowly eat: you would have to add to (the donut) to the question and it to the answer. On the other hand you can have again What did she do slowly? — Eat a donut, so ate a donut is a constituent.
What you are actually doing when you replace slowly ate with ate is testing the omission of slowly. This test works especially well for adverbs and adverbial phrases, and correctly suggests that slowly is a constituent.