Also try opening a checking account with Chase to establish a relationship. I applied for the Chase IHG one in Jan and was declined. I then opened a checking account with $500 / mo direct deposit in April. I applied for the same card a few weeks ago and was approved. Credit score about the same as back in Jan.
For the cards you mentioned, you can also go into a branch and see if they can do a pre-approval, so you know you're not wasting your time.