I went to BLS site (as well as Googling with site:bls.gov) to see what very detailed data I could find to help me benchmark software engineer compensation.

I didn’t find anything usable. Could you send a URL for data for a company who wants to understand cash plus equity competitive positioning relative to the top 10 highest-paying large SWE employers?

Navigaton on the site isn't great and that's a fair criticism. Software jobs salary data is here and you can drill down to state level etc https://www.bls.gov/oes/current/oes151252.htm