You should be okay. I highly recommend you have an attorney help you make your case to the USCIS Officer.
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It is your burden to prove lawful admission.
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Not a huge problem if it's the way you describe it. You have to prove you were lawfully admitted, but the combination of the faint stamp and tickets suggest you are probably ok.
This is not legal advice and no attorney-client relationship has been formed, now or in the future. This is just a casual opinion expressed about a hypothetical situation.