The recent late payment is def holding you back. What other derogs you have on your reports? Your scores are pretty low for only having 1 30 day late from 12 months ago.
With your BofA card they likely won't unsecure because of the late payment which was with them. With the savings why not try to up that limit or open another secured card with a higher limit?
After a couple years distance from the late pay you may start getting better luck.
Have you tried Barclays yet? I imagine you may get over 1,000-1500. Maybe apply next month (12 full months from late payment)