a. Whatever materials you send to the university committee and the provost, such as sample work, should be vetted by one of your faculty. Someone in the committee might actually read the materials!, and it there are problems your case is much weakened. The X school has people on the faculty read the various pieces and write memos about them, criticizing them, evaluating them. One piece per faculty member.
b. Unread books. A sure road to disaster is not to have read the book or book ms with care, or the papers. In one case, it was clear that no one of the referees or in the department had read the ms, while they raved about its excellence.
c. Unmet objections:A concern re problematic statistics could readily be handled by someone finding out what is wrong. But someone has to check it out. Now is the time to catch problems, not in central administration. That supposedly-rigorous folks are willing to let the candidate off, since the candidate is not in their field, is amazing. That they then would say that maybe it was the co-author who made the error is the kind of account that devalues all of the vita.
d. The committee must address trajectory issues, especially for tenured appointments.
e. As for reputation and publication venues and prizes, of course they matter, lots. But unless you read the work, and many referees only read the CV and spit it back, rarely engaging with the work itself, your letter or the dossier are weakened.

I am quite willing to have the dean say, I want this X for purposes of school development, and the dean to take responsibility for it.But you don't want to use up your credibility, cred that might be spent on truly important cases.

The committees often have very astute members, who are eagle-eyed in reading the dossier, and as a group they find most of the problems quickly enough. If they are social scientists, they demand of others what they demand of themselves. They know which schools and departments tend to be reliable, which are not.

Finally, no letters from advisors or collaborators, except to testify as to the nature of the collaboration. Arms-length "textured' letters are best. Criticisms are fine.