***** NOT A TEACHER *****
Hello, Jason:
First, congratulations on asking a question until you receive a reply that satisfies you. You are an excellent student.
Several years ago, I posted a question at another grammar helpline. One moderator very rudely criticized me, for he had discovered that I had posted the same question on another helpline. A fellow moderator of his then told me that, of course, I had the right to post my question on as many helplines as I pleased. So if you do not get an answer that pleases you, you should definitely feel free to ask at one of the other grammar helplines.
Second, I cannot answer your excellent question.
Third, I found a sentence that may (may) give you a little (a little) help.
a. "My father has a house to rent."
i. The book says that the object is "house."
ii. "to rent" is an infinitive phrase/clause.
iii. And, yes, "to rent" is an adjectival modifier of "house" -- the book tells us.
Fourth, but don't get too happy!
The same book gives this sentence: "We thought him to be the best player.
a. The book says that "him" is not an object. It is the subject of the infinitive. "Him" = "We thought that he was the best player."
b. The book does NOT say so, but I assume that the book would NOT classify "to be the best player" as adjectival.
Fifth, I will stop here.
Maybe the above information (which comes from a reputable book) can help you to answer your own question. I certainly do not have the confidence to do so.
Hopefully, someone here (or at another helpline) will give you the answer.
Authority: Pence & Emery, A Grammar of Present-Day English (1947).