Your claims is that the book of Hebrew is part of the general epistles with the reasons you have given which is good enough. However, you also alluded to the fact that some thoughts expressed or revelations given in Hebrews share likeness with some of the revelations of Christ in some of the Pauline epistles. I totally agree, however, you concluded that that wasn’t enough to prove that Paul wrote the book of Hebrews but, that the similarity of revelation could be based on same doctrinal stand of both Paul and the writer of Hebrew.
Not disregarding your stand but drawing on further similarities or traits in Paul’s writings, I would like to suggest even as some scholars assume to be the case. That the book of Hebrews could have been authored by Paul. Now, the writer might have not been Paul but anyone. However,the thoughts conveyed or the message communicated might have been Paul’s.
Now, even in these present times we have what is known as ghost writing. An author of a book can contract a ghost writer to pen down his thoughts. At the end of the day, the author of the book wouldn’t be the ghost writer but the author of the ideas. Because the ideas form the text.
Now, those traits or possible pointers to be considered for Paul to be seen as the author are:
1. The same greeting or nature of benediction with Paul is what we see closing the epistle of Hebrew, “Grace be with you all. Amen” Hebrews 13:25. And Paul had said in 2 Thessalonians 3:17-18, ” I, Paul, write this greeting with my own hand. This is the mark in every letter of mine,it is the way I write. The grace of our Lord Jesus Christ be with all of you.”
2. The author of that work said in Hebrews 13:24, ” …they of Italy salute you.” Paul was at Italy at some point in his ministry and could it be that was when he authored the epistle to the Hebrews? Possibly.
3. The epistle to the Hebrews made mention of Timothy who was Paul’s son and companion in most of his ministry journey. Which again could be indictive of Paul writing or authoring the epistle of Hebrews.
Although, the epistle didn’t start with Paul’s normal way of greeting but it ended with how Paul said he will always acknowledge his letters. So where the usual introduction of the Pauline epistles could show that Paul wrote them, it is safe to say that the way he said he would indicate ownership of his letters in closing, should also hint us strongly that he wrote or authored the book of Hebrews.