Since Chicago is already on your list, you might try something like this:
- Apply by deadline: ED (Columbia or other like Barnard)
- Simultaneously apply EA Chicago
- If deferred or rejected by ED school then convert Chicago EA app to ED2
- By Jan 1 apply to the rest of your schools in the RD round
This gives you three shots on goal during the early round. Getting into Chicago EA is probably harder than Columbia ED. But the EA app shows interest, moreso than just applying ED2 straightaway.
Keep in mind that financial aid is a big factor. Are your parents willing to shell out over $320K for an undergraduate degree? The ASU honors program at only $2k per year sounds like an awfully good deal.