NOTE: Please see my take at the bottom, even if you don't want to look through the data.  It's marked in a different, larger font so you can skip to it if you prefer

Looking at the total output, as measured by http://nturanking.csti.tw/, which is generally the standard for these things, here's where BYU falls among PAC12, Big12 and other discussed expansion candidates:

You'll note that (with the exception of UNLV and possibly Oklahoma) R1/R2 designation (which looks at $) corresponds pretty closely with output.  If you're top 450 or so in output, you're Tier 1, then 450-550 is a mix of Tier 1 and Tier 2 and everything below that is Tier 2.

For what it's worth, if you look at BYU's ratings broken down by subject (available at http://nturanking.csti.tw/ranking/bySchoolName/Brigham%20Young%20University), you're correct that BYU's strongest research areas are psych, economics, social science, computer science and mechanical engineering, just as you suggested. But even in the best of those, they're not top 200.

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Which again I'll emphasis is FINE.  BYU has a different mindset and prioritizes education over research.  Frankly (despite being in academia myself), I think that's better than how most universities approach it, and it's one of the things I value about BYU.  We're different; let's embrace and accept that instead of continuing to take offense that we don't do as much research as schools that prioritize that over education.