Wirelessly posted (BlackBerry: BlackBerry8530/5.0.0.1030 Profile/MIDP-2.1 Configuration/CLDC-1.1 VendorID/417)

"We don't have particular destinations, but often do last minute trips to MIA, LAX, LGA, and SEA."

Then I must confess that I am puzzled why you could not get good value from your Chase UR points. UR points convert to BA Avios on a 1:1 basis, and 7,500 Avios get you a one-way from DEN to LAX on AA, or from DEN to SEA on AS. DEN-MIA on AA would cost just 10,000 Avios.

Of course, you'd have to find lowest-tier award seat availability on nonstops to get those redemption rates. Notably, however, BA does not charge a fee for close-in award bookings.