How can I get Apple to unlock my iPhone so that I can switch carriers?

Apple doesn't unlock iPhones at all. They don't have the legal right to do that.

Only the carrier it is locked to can unlock it.

See this document: https://support.apple.com/en-us/HT201328

Apple doesn't remove carrier locks. Ask the carrier it's locked to if they will.

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How do I Unlock my phone

Did you bother clicking the link the the post above yours?