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Good Luck!!
LUCK!!!!
I would say apply for the Ring card and if Declined call Recon...They may approve you for the new card or approve and move your CL from the rewards car to the Ring and close the rewards card.
I suspected they would say no. Though I was told no about 4 times before I got my Apple Visa PC'd to a Rewards MC, I speculate that they will only allow changes into the Rewards card from their other cards. I was offered only a choice of the Rewards MC or iTunes Rewards Visa(Same product type as the Apple Financing).
They wouldn't split your limits for you? (If you even cared about two smaller limits or one bigger one)
Why did you want the Ring? I've been doing some research on it and it isn't that great unless you plan on carrying balances.