sense of what's required
That's the problem. It's a crap-shoot unless there is an established policy - usually only for NMSF. A top oos public doesn't need to attract oos students unless it's from an geographic area underrepresented. At the next level, I'd say, high stats kids are considered for merit aid. Considered- maybe yes, maybe no. And until the money runs out. Apply early. DC got $15,000/yr from a top 20 oos public however was not invited into the honors college, whereas friend from same HS got into the same U and into the honors college but no merit money. It is so random.
Now for a lower tier U's (say ranked below 70 USNews National U's- and especially the close you get to 100 and beyond) I would should ask them directly. They want oos students. Some will give in state tuition to oos with very average stats.