It's been a while
Another couple of Audio Engineering Society conferences, and some conversation over a pitcher or two of beer resulted in no amazing new information as to who might have been The Beatles live sound engineer, but did result in quite a lot of "conceptual" ideas about sound engineers and sound engineering within the time frame that The Beatles were touring and playing live.
In effect, my initial post in this thread attempted to overlay the modern concept of sound engineers who tour with a specific band, either working for the band directly, or working for the PA company - but with the band for their entire tour.
It would seem, by all the information gathered to date on the subject of "who mixed The Beatles live"
, that the actual title of Live Sound Engineer
just didn't exist in a standalone manner during the time the lads toured and played live.
Rather, as confirmed somewhat in earlier posts in this thread, all such technical "extras" like sound and lights were primarily handled by the venue themselves, operated by venue employees, mostly with equipment they owned in-house ... the venue being asked to hire in extra equipment locally to augment the house PA if Mal deemed the existing venue PA too small.
A very telling aspect of this entire discussion is simply that The Beatles flew from gig to gig on commercial airlines, carrying everything they needed with them on the flight. There is no record I've found which would indicate that there was any trucking involved in their later (and much larger) tours. No record of any transport vehicle moving about North America hauling PA and/or lights and staging, or band equipment (as was extremely common with tours beginning in the early to mid-seventies onwards).
It would seem that everything
the lads needed onstage (guitars, amps, drums, etc) was able to be moved within the luggage compartment of a commercial aircraft.
The original club tours of Europe would have involved a Commer Van hauling equipment, and driven by Mal, but certainly the later Beatlemania tours don't seem to note any trucking information.
If there was
trucking information which remains undiscovered, that would certainly be a critical bit of information, and what
they were hauling would answer a lot of (currently unanswered) questions.
So still, these few years after my original post - it would appear that the answer to my question in the first post of this thread is simply that Mal directed local venue personal both in advance, and on-site as to how the stage was to be set, how the live sound system was to be operated, what lighting was required, and then went on to direct the concert itself in terms of getting the band to and from the stage, getting the concert started, and on to how the concert proceeded to its eventual conclusion ... getting the guys out of the venue and back to the hotel.
The short answer would be that the lads literally just missed
the era of a dedicated Live Sound Engineer traveling with the band.