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I already had a sapphire preferred card so I product changed it to a freedom unlimited. Applied for CSR the next day but got a 30 day message. Letter said I already had a sapphire product. Called up recon and they verified my preferred was indeed changed and approved the application.
So just beware if you want the auto approval it may take a few days before you can apply after product changing another sapphire card.
Chase allows you to pretty freely move your CL between various cards, so you would be better off applying for a new card to get the bonus, and then moving some of that CL over to your CSR.
Also, min APR on CSR is 17.49% so not sure how much you could get it lowered.