Provided the system is as up-to-date as they claim, you should have been unable to get an eTA. Applying for an eTA could have, in theory, triggered an investigation into your status but I can't be sure about that. It's possible that people who landed decades ago and have never applied for PR Cards are not in the eTA system as permanent residents. That's just a guess as to why you were able to get an eTA. As to whether or not you should use that eTA: that is a question for a lawyer or a Regulated Canadian Immigration Consultant. As a PR, you're not entitled to have visitor status, so I don't what kind of impact entering Canada as a visitor would have on your attempts to get a new PR Card.
I don't understand how you can enter Canada without an eTA (or a visitor visa) and without showing your landing paper. Basically, only Americans can travel to Canada without that stuff. You have two choices:
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[*]Fly to the US with your landing paper, drive to Canada and hope they let you in and do not revoke your PR
[*]Use your eTA to fly to Canada and enter as a visitor or a PR, depending upon what happens at the interview - again, hoping they let you in and don't revoke your status - and hope that, if you are admitted as a visitor instead of a PR, it doesn't have an impact on your PR status.
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Unless there's some information I'm missing, I don't know what other choice there is. As to which one to take, my guess would be the first but I would strongly suggest you speak to an expert about choice number 2 if you are seriously contemplating it.