I’m glad the card is arriving soon.
In case anyone reads this later on I wanted to share a somewhat similar experience of a green card arriving while the GC holder was out of the country:
After my wife entered for the first time with an endorsed CR-1 visa with an I-551 stamp good for a year, the physical card took 4 months to arrive and as a result came in the mail when she was out of the country. When she returned to the US, the airline rep was confused with the still-valid stamped visa and called the number for (I think) CBP where the person on the phone wanted to know why she didn’t have the GC that had been issued. Although it took some explaining, eventually everything was fine. She was told that the next time she traveled she needed to use the GC instead of the stamp. I don’t see why there actually would have been a problem traveling with the stamp again while it was still valid, but we didn’t need to find out.
Based on that one would imagine that the expired GC and a still-valid extension letter would work the same way even after a new GC is issued, although if using that to travel it wouldn’t hurt to budget some extra time for the check-in process at the airport.