I would say your logic is flawed.
A) The letter of Hebrews isn't to a "narrow audience". It is a letter to all Hebrews.
B) It is refreshing to hear a Catholic claim that Paul's writings was inspired. It has been my experience here that not all Catholics believe that. Be that as it may, the mystery of who wrote Hebrews doesn't make it any less inspired. We certainly wouldn't say Ruth, Esther, Job, Jonah, etc. aren't inspired even though we don't know who the author is. There are many inspired writers, not just Paul. Some we know, some we don't.
C) I see nowhere in the letters of Peter where it claims Paul wrote Hebrews.
No, this is not correct. The book of Hebrews is addressed to Christian Jews who need to know how to teach the meaning of the Hebrew religion of the Old Testament to both non-as-yet-regenerate Jews (to bring them. like the Bereans, under convicrion) and to regenerate Gentile disciples (for their maturation in the whole Bible). Hebrews Chapter 6 is very explicit on this, and is summed up in verses 9 and 10:
9 But, beloved, we are persuaded better things of you, and things that accompany salvation, though we thus speak.Your opinion contradicts this passage, and colors your other opinions about the issue.
10 For God is not unrighteous to forget your work and labour of love, which ye have shewed toward his name, in that ye have ministered to the saints, and do minister.
C) I see nowhere in the letters of Peter where it claims Paul wrote Hebrews.
It is correct that Peter did not say directly, "Paul wrote the book of Hebrews." It would take the compilers of the New Testament canon to do that, but they themselves coyld not write the inspired words, either. So we must infer, as I already showed quite logically, from what was written in 2 Peter 3:15 and 16 (which itself is inspired Scripture, whether written by Peter or not), that all Paul's epistles were as much inspired Scripture as any of the canonical books of the Old Testament (the Tanach), which Peter calls "the other Scriptures," and Luke calls "the law of Moses, and the prophets, and the psalms" (Lk. 24:44).
You are not seeing that the primary audience of Hebrews was all Christian Jews everywhere for all time, whereas the audience of 1 Peter and 2 Peter was all Christian Jews located in Asia Minor, in the very target area of Paul's evagelistic routes, and therefore a subclass Of the target audience of the epistle to the Hebrews.
Furthermore, the writer of the 2 Peter verbally inspired infallible Scripture says that Paul wrote (obviously an epistle) to them, the "you" who must be at least the same identical "you" that 2 Peter addresses. So either: (a) Paul wrote to them another inspired letter(s), a Scripture separate from the book of Hebrews, and it had been lost after the time 2 Peter was written but before the time the canonical compilation commenced; OR (b) the book of Hebrews is the epistle written by Paul to which 2 Peter 3:15 refers.
There are no other options for what appears in that verse and in verse 16.
From the sense of what you wrote here, I get the notion that you have not taken the time to do yourself a favor and carefully review the paper at the link I gave you, which was written for the doctoral work, submitted, carefully examined, and accepted toward the degree of the author of that site. Not to do so will leave you uninformed of better, more detailed research and conclusions than you've posted here.