For need based, don't count on it, even though you have a low income, you're OOS and it's a public college. The only scholarship you're likely to get is
Dean's Scholarship | University Student Initiatives
I don't know anything about it, but you seem to have good stats, so.
Just curious, but why is ASU your safety, if you're OOS?
For when to apply, there is no disadvantage, that I know of, to applying later. I did, but I was also a NMF, which changes things. But I don't think later will hurt as long as you make the deadline.
What other schools are you applying to?