If you lower Chase CLs, just note that the SM rep will tell you the new limits are effective immediately and show on your Chase accounts, but the lower CLs don't reflect on your credit reports until Chase reports them after the monthly statement closes on each card, or you pay off a card in full. It's debatable whether you're good to apply right after Chase reduces your limits as requested (it's in their system), or you should wait until Chase reports the lower limits to your credit reports (what Chase sees when they pull your credit reports). If you really think you're pushing your limits, it's probably better to wait until your credit reports show the lower limits.
Also note that a CSR approval typically comes with a high credit limit, as much as ~$20k-30k+. You need only $10k to open a CSR (Visa Infinite), and $5k to open a CSP (Visa Signature). If the the additional extension of ~$20k-30k+ credit on the CSR takes you >50% of reported household income, the CSR CL may affect how much more credit Chase will be willing to approve for the CSP.
Turns out, you don't need to call in to get the first card (CSR) approved if not auto/insta-approved. The important part is to apply for the second card (CSP) the next calendar day after whenever the first card is approved, and preferably get that second card approved on the same day as you applied. There are some mixed DPs, but I think if you leave the second card's approval in Chase's hands there's probably a higher risk of it getting declined if and when they see the first card in their system. If the second card is not auto/insta-approved, I would call recon and ask if there's anything you can do to help get the card approved. The recon rep may or may not see the first card in the system, so ymmv -- if the rep is well informed about the one Sapphire rule, they may give you a hard time, but they can push the second app through; if they won't, HUCA. If the rep doesn't mention the first app, or is just not well informed, then approval may just be a matter of verification or moving credit around (ideally from a card other than the just approved CSR).
Is the card showing closed? Closed cards can still appear on your online account unless you "hide" them.
Good luck!