Ideally, the Linden Home's auto-close door setting would not only be announced by link message to the home's own scripts but be accessible to unlinked, user-created content on the parcel, including the "Extra door" items in the Content Creation Pack.
But failing that (and it would be a more general solution anyway), the door script should be open source —or at the very least the sound assets provided, by UUID if nothing else—so we can replace the script ourselves but still maintain consistency with other doors in the build. If the user writes the script they can make it auto-close or not, but still it would be best if user scripts could access the current auto-close setting for the house-linked doors.
(I'm working with the Ridgewood Enclave theme but presumably all themes frequently get user-added doors.)