I have PBS performing the Schubert sonatas on period instruments and agree that the mechanical noises are appealing in order to get a feel for what the instrument is doing and how that affects the performance of the music; this being in addition to the clarity of the registers in the sound. And it is this clarity, as you mentioned, that is so valuable when hearing the differences between similar interpretations of keyboard music.
I could see that complaint of Brautigam's interpretations where much of the focus is on speed and dexterity. Generally, I too prefer more variation of tempo choices rather than it always being quick. However, he does have a way of pulling you in through sheer virtuosity where one finds it hard to not be awed by his playing. I would say this is definitely more of a merit than a detraction from his playing.
I look forward to your upcoming thoughts.
I do enjoy those PBS fortepiano recordings of Schubert very much as well. So much so that I ended up buying the old Astree CDs of Schubert's works that weren't included in the Arcana box.
Onto the thread topic -
For frame of reference my favorite large cycles are Geza Anda and Murray Perahia. I have read many opinions that Camerata Academica des Salzburg were not a great orchestra back when Anda recorded his cycle. For the life of me the only thing I can hear "wrong" with them are they are not the most dynamic orchestra, I really struggle to hear more at fault with them than that. And because I have listened to this cycle for so long when I hear them with Sandor Vegh/Schiff when the orchestra was much better the orchestra playing is so extremely dynamic that it is hard for my ears to get adjusted to this; it almost sounds like an orchestra scored for some of Mahler's larger symphonies in comparison! (hyperbole) . This is a deficiency on my own part there is no doubt that Sandor Vegh does an extremely fine job with them, it's just not to my taste in the early piano concertos. And in the more popular, more recorded works there are more characterful pianists I find myself liking than Schiff. For me Schiff really came into his own by the time he started recording with ECM, albums like JSB's Partitas are pure stunning musicianship that I don't hear on early Decca Schiff who is more conservative and less adventurous.
With fewer recordings I enjoy ones from Fazil Say, Rudolf Serkin, Peter Serkin, Wilhelm Kempff, Leon Fleisher, Friedrich Gulda and Edwin Fisher just off the top of my head, there are many more that have recorded fine Mozart Piano Concertos, this is repertoire that is "pianist's pianist" type music.
Now onto HIP:
I am not so sure I hear a vast difference in piano sound from either Malcolm Bilson or Ronald Brautigam. Both have a characteristic modern reproduction fortepiano sound that is light on bass and more tilted toward the upper midrange and treble. For me at least I do not hear a large enough difference to make this a meaningful thing in choosing one cycle over the other. If someone has particular segments or works where the differences are really large please mention them and I will jump to them.
One reviewer actually thinks that Bilson is more convincing than Brautigam:
https://www.classicstoday.com/review/review-16185/
And in Hurwitz's video lecture series he chose Bilson as the reference HIP choice. There is also Immerseel on Channel Classics though this set is out of print, it does turn up used and isn't that hard to find. I haven't heard it.
Where I am interested in hearing people's thoughts is on interpretation between Bilson and Brautigam. I've listened to 24/25 from Brautigam and I'm not really hearing any orchestral deficiencies here either. With the context of it being a chamber orchestra and their natural limitations.
I've been listening on my laptop with headphones since I don't own either of the cycles, I've been trying to determine which one to buy.