If you could configure the common shells (bash, zsh, fish) to run a custom command on submitted shell input before executing, you could build a heuristic function that would attempt to recognize when you were pasting in a prompt. Unfortunately, I'm not aware of such a capability, as it would be useful in a number of situations.
Another alternative is to put the octothorpe # at the beginning of your prompt - then you can keep your > at the end.
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