AFAIK Chase isn't churnable. I have received offers to upgrade my UA card, I think it's the basic one which I also have had for many years, to whatever one it is that earns 5K RDM bonus/year (but also costs $30 more in annual fees). I guess you could upgrade to the RCC version.
How about applying for the Continental credit card? Those miles will eventually be UA miles, whatever the new UA miles program is called. If you apply for the CO Mileathon and apply next month, it will count towards Mileathon credits.