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Personally, if this card interests you and fits your lifestyle and spend, I would accept it. Keep in mind, the assigned SL is based on a variety of factors and just because you have other cards >$10K doesn't translate into Chase approving or matching anything higher. It's all profile dependent.
If you accept the terms with the SL as provided, yes you would incur another HP for a CLI at activation. That said, you can always reallocate CLs between Chase cards without any HPs. You can explore the option of going to the branch, but it's highly doubtful much would change, about the only possible change you might see is the pricing (i.e. APR), but YEMV.
From what I have read, a CLI right after will incur another HP.
Have you considered the CSR?