Just checked the (nginx) server logs for cardbook access. However, from the logs there is no difference to tell between the requests from Thunderbird CardBook/41.5 Lightning/68.0 (known issue) and Thunderbird CardBook/37.6 Lightning/6.2.9 (working): a couple of PROPFIND and REPORT, all resulting in a 207 (not a single 503).
But as mentioned before: server communication and cardbook worked well (even after several restarts address books remained) until additional e-mail accounts were added to the Thunderbird profile.
Maybe this information helps (TB 68.0, cardbook 4.51):
upon configuration (first run, abook displayed):
TypeError: db is undefined 176 cardbookIndexedDB.js:86:22
after restart (second run, abooks gone):
SecurityError: The operation is insecure. cardbookIndexedDB.js:30
I was not able to reset profile (indexedDB etc), so I finally created a new profile. Here cardbook worked for a while (i.e. abooks were present even after restarts), but after further profile migration (added more e-mail-accounts, calendars etc.) it ended up with the same issue.