Adverbial Clauses & Subordinate Conjunctions

In the book Grammar for English Teachers Second Edition, it states in a table on around page 390 that "despite the fact that" is a subordinate conjunction. According to a few dictionaries that I checked, despite can be a preposition, noun, or a verb, but it is not listed as a conjunction. But that got me thinking, though, about adverbial clauses that introduce dependent clauses and subordinate conjunctions that introduce subordinate clauses.

An example from Chicago Manual of Style is as follows:

• I bought a car despite my father's warning not to. The despite-clause modifies the verb bought. It's an adverbial clause.

We could rewrite this slightly to incorporate "despite the fact that" as follows:

• I bought a car despite that fact that my father warned me not to. The despite the fact that seems to join two clauses, with the latter clause being subordinate.

Now, we could rewrite that sentence using a different subordinate conjunction as follows:

• I bought a car even though my father warned me not to. The even though is a subordinate conjunction.

I think I might have answered my own question. When despite the fact that and even though were used, the clause that followed was identical in both cases—my father warned me not to, which is itself a subordinate but independent clause.

When despite is used alone, then it introduces an adverbial clause. In the first example, despite my father's warning not to is the adverbial clause.

So this wordy phrase despite the fact that functions as a subordinate conjunction even though it can't be found in a dictionary.

Can anyone comment on my thinking? Am I way off base, or did I more or less get the proper understanding?