It’s nothing more than speculation from both us. I’m not, however, persuaded by your arguments.
Mozart was an extremely prolific composer; that’s historical fact. Copying scores (let alone composing them) is extraordinarily time-consuming and requires a great deal of mental focus. That’s also historical fact, and is something I’m familiar with first hand. I can hardly believe I have to mention that these details are very well-known, and part of the historical record. Mozart absolutely had to spend a vary large amount of time at the composing desk. Also maintaining an active career simultaneously as a keyboard virtuoso would simply compound the demands on Mozart’s time. Do I really need to provide a cite for these points? That seems very silly.
I did spend some time researching musicology articles from JSTOR tonight. I also reviewed a biography of Mozart (Solomon) and consulted a musicologist friend of mine who is a specialist on Mozart. For the record, I did this little bit of research because I’m genuinely curious about the question.
Neither the articles (six or seven of them about various subjects such as Mozart’s instruments, his teaching of intonation and tuning systems to private students, and so on) nor the biography have anything to say whatsoever on the issue of who did the actual tuning. An article on the degree to which Mozart’s monetary problems were due to overspending turned up nothing about his hiring a tuner or not, although it make a general observation that Wolfgang and Constanze were accustomed to a standard of living (including the hiring of household staff) that was frankly beyond the means of either of them in the last half-decade or so of Mozart’s life.
It appears to me that the issue of tuning instruments in Mozart’s household has not been raised nor resolved by musicologists. To resolve the issue at this point would seem to require primary source research. Since I am not a musicologist, I’ll leave that to someone else.
My musicologist, Mozart-expert friend similarly had neither heard of nor read anything concerning whether Mozart tuned his own pianos or not. He commented that it was a good question, but he also agreed with me that Mozart was so busy composing and concertizing that he would likely have turned to hired help to keep his instruments in tune, except for possibly occasional touch-ups, which I allowed earlier. Obviously you weren’t in on this conversation, so you’ll just have to to take my word for it.
I conclude that without more research into primary sources, this question is not definitively answerable at this time.
However, I still think it was unlikely that Mozart habitually tuned his own pianos as a professional musician, say from 1773 on.