Hi Jean,
the tuning sounds good! Of the swaying unisons, only C5 comes across as a bit sour. Luckily, it's not used much
I'm not familiar with Prambergers, but I'd guess it's close to the break?
Anyways, the tuning stability seems good if it stays pretty much in the pocket for a week! What kind of weather do you have in Quebec? I'd guess it's as much of a challenge for a tech as what we have here, 3° F as of now.
There's no substitute for high-quality mics, but here are a couple of suggestions:
From the recording and what you write (mic position rougly 30" away from the strings), I suspect the lid might be interfering somewhat? Budget cardioid mics have a rather nasty off-axis sound - that is, any reflections hitting the mic from the side or from behind are going to sound less desirable. This is due to the cancellation properties of a cardioid mic. Sound off-axis are let in through "a back door" (holes in the side), and thus ideally hits the diaphragm at the same time from the front and the rear -> no sound.
Keeping this cancellation uniform across the frequency spectrum is hard, not to say impossible, to control. Higher frequencies are more delicate than lower frequencies, because of the shorter wavelengths requiring more precision. As a result, some frequencies are boosted while some are attenuated, creating more of a "comb filter" than an actual cancellation. The more expensive mics have less of a comb filter, because of the great care in build and materials. DPA MMC4011 would be one of the best, somewhat of an industry standard.
A closer mic placement OR mics placed further away are usually giving you a better end result. If you go close, that would be roughly 10". Difference in amplitude between the strings residing close to the mics and the ones further away is an issue, but it is not as troublesome as one might be led to believe. The body of the sound comes from the soundboard, not from the strings themselves (a fact that you as a piano tech no doubt are well aware of).
If you go further away, a good choice might be a stereo mic pair mounted to one of the broadcast standards (NOS and ORTF come to mind, in a subjective order of preference) about 30" from the piano, at half of the pianos length, pointing towards the lid hinge closest to the piano player. Another nice spot is approximately 15" above the piano player's head, pointing down towards the strings. I personally like that placement, because it's the way I'm accustomed to hearing the piano, and it also gives a L/R sensation of the bass/treble. This is for solo piano. If there are other things recorded at the same time (as I believe is the case here), a close mic placement might be the best choice.
At last, just out of curiosity, I have to ask if you might remember what color the lead vocal mic was? It sounds like a SM Beta 58 (silvery blue), but it might also be a classic SM 58 (dark grey), if presence was boosted in the mix.
Aah, I get nostalgic... my first nerdy passion (sound engineering)...