The receipt is not a proper I-9 document so it will be up to the employer whether accept the notice until your green card is received.
I would advise the employer not to employ you without the card, doing so will represent a potential risk to the employer.
This answer does not constitute legal advice and you should contact an attorney to confirm or research further any statements made in this answer. Any statements of fact or law I have made in this answer pertain solely to New York State and should not be relied upon in any way in any other jurisdiction.
It really is up to the employer. However, the ead or the green card are the correct documents. I understand why you wouldn't want to renew. If it is only a day a way maybe its better to wait one day and see wht the employer says. Why renew for the purpose of that job if they won't hire you anyway? If they are willing to work with you they will say so and then you could worry about renewing.
You should file for a replacement of the lost card. Meanwhile show the documentation that you do have to the potential employer, explain the loss of the original card and that you have filed for its replacement.
This answer is of a general nature and does not in any way create an attorney-client relationship.