You're overthinking this. Most of those (I did accidentally include GS-12 in my search, didn't mean to, so a couple jobs cap at GS-12) have a pay grade spread f

You're overthinking this. Most of those (I did accidentally include GS-12 in my search, didn't mean to, so a couple jobs cap at GS-12) have a pay grade spread from something like GS-7 to GS-13 or even GS-15. You wouldn't be getting hired in at anything below GS-12 if you've got more than a year or two of professional experience and a degree. And if you've got a masters degree and 10+ years of experience, getting hired in at GS-13 is not too hard a sell anymore (it would've been a decade or so ago).