If you could fill out your profile, it would be a great help to the community: https://www.visajourney.com/timeline/profile.php?id=490476
The Department of State, who determine eligibility and issue visas processed at embassies and consulates, have the information regarding K-1 visas here: https://travel.state.gov/content/travel/en/us-visas/immigrate/family-immigration/nonimmigrant-visa-for-a-fiance-k-1.html . The important part is in blue - K-1 visas are a single use only visa. You enter the US, you must marry and file AOS within 90 days of that date of entry. You cannot leave or you invalidate that single entry visa.
Additionally, the DOS lists the criteria for AVR here: https://travel.state.gov/content/travel/en/us-visas/visa-information-resources/visa-expiration-date/auto-revalidate.html#:~:text=Nonimmigrants who departed the United,Departure Record%2C endorsed by DHS. and lists F, J and M visas, but not K visas. IMHO, I suspect it's going to be an extremely challenging sell to try and pitch AVR when it's clearly stated that a K-1 visa is a single admission into the US and the categories of AVR eligible visas are limited. Typically, if people leave before they marry and adjust status, they have to start at the beginning of the application process and go through the wait times as they did in the first place.
In the e-mail you received from CBP, it says:
You would be marrying and filing for an adjustment of status, thereby not intending to resume the same non-immigrant status.
IMHO, I suspect it's going to be an extremely challenging sell to try and pitch AVR when it's clearly stated that a K-1 visa is a single admission into the US and the categories of AVR eligible visas are limited. Typically, if people leave before they marry and adjust status, they have to start at the beginning of the application process and go through the wait times as they did in the first place.
Apply and come back to the forum and let us know how you make out. I'm certainly interested!