You have several new accounts that don't show up yet with fairly low limits, a recently paid off collection that was not a paid for delete, and no older established high limit cards, although you do have an on time mortgage. But your scores are in the poor/fair range because of the collections.
I would chill for right now, let the new accounts report, keep your debt ratio at no more than 20%, and see where you are around June or July trying for a cli on the new cards, and letting the cli's show up on your bureaus before going for Am Ex.
