Unfortunately Chase has a long memory and that may be an issue. Only way to really know is to app when ready, it shouldn't be a HP if your blacklisted.
what were the reasons for denial with chase?
You really should have at least one credit line reporting with at least a $5,000 limit on your reports before you go after the Cash+ card as it is a Visa signature card, or even the Chase Sapphire Preferred since that is also a signature card.
Amex might be your best strategy - app for the BCP and if approved, ask for a 3x CLI in 61 days. That might be the quickest way to reach the $5,000 limit, and then you could pursue the CSP and Cash+ cards.