Yes, your analysis is correct for both sentences. " "Could have" makes sense, but doesn't sound as natural to me as a native speaker. Hope this helps.
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I left the papers on the table so she could see them. = I left them deliberately in order for her to see them. I wanted her to see them. yes
I left the papers on the table so she could've seen them. - I think that 'could have' in this example means something like 'might have'. yes So, she might have or might h