Okay, here's the scoop from the ARE. I got a return call around 1330 EST today, but didn't talk to the fellow until after I returned from the fields later this afternoon.
We both win and lose, I guess - or need to take a lesson in talking past each other.
The 14,000+ readings the ARE has available online are not complete - not yet, anyway. More readings are/will be added over time, but never the complete 30,000, since there are incomplete or missing records for a portion of those remaining readings. The fellow I spoke to said that the primary problem in adding readings is the time and effort involved in transcribing them from the original carbon copies and formatting them for online disbursement (that seems reasonable). He did indicate that the ARE has already put the most interesting readings out there already, but he hopes the total will eventually be between 20,000 and 22,000.
Cayce's sons got the 30,000 figure (the figure I understood) from Cayce himself, who references the number in four letters and two lectures he gave. The letters and lecture transcripts are available at the ARE. The same figure was given to me and my friend Jon by the archivist all those years ago, but he clearly meant Cayce's reckoned number, and not the number currently available online.
So, if Cayce gave 30,000 readings, it was by his own reckoning, but that number will never be realized at the ARE, thanks largely to sketchy transcription of the readings prior to 1925 (many of these readings were done by return mail, and are in the possession of the recipients' estates [if they exist]). The good news is that the ARE receives a fairly steady stream of newly-discovered Cayce material, usually from family archives, estate sales, etc. There are more than 14,000-odd readings, but they are only transcribed as material is available, and we apparently have - in the ARE's estimation - the most salient material.
I guess we now retire to neutral corners. There are good records for 14,000-odd readings, plus another (perhaps) 5,000 or more that may be added in the future. Cayce reckoned himself at 30,000 readings, but many of these are now unrecoverable.