So, I'm curious about the validity of the underlying assumption
in this whole piano roll tempo discussion, to wit, that there is
a "correct" tempo.

If one listens to performances of any piece of music -- be it popular
or classical -- the tempo, chosen by different artists or by the same
artist at different times, varies wildly.  Sometimes this is true
even when the performer is the composer who you might think was the
ultimate authority.

Things get, I suspect, even more complicated in the world of mechanical
music, where people other than the artists are involved in creating
the final product and may have motivations other than purely musical
ones -- roll lengths, perforator sizes, cost of paper this month, or
whatever.  Then at playback, most pianos are different, certainly now,
and I suspect when they were new as well.

Most instruments I've seen play faster or slower by the few percent.
The differences being discussed in this thread depending on how
heavy-footed you might be or on the exact design and adjustment of
the system.

I'd suggest that, except in very rare instances where an artist
insisted on a precise tempo, that these markings are suggested starting
points, based on what a series of people involved in making the product
decided at various points in the process.

I wouldn't be shocked in the slightest to hear that, after a roll
was produced, the marketing guy had come in and said, "We can't sell
a two-dollar piano roll that's under two-and-a-half minutes long,"
and the factory guys said, "Okay, I have an easy fix for that: just
change this Tempo number printed on the leader!"

I'd strongly suggest setting the tempo to something you like and enjoy
the music.  Discerning what is "correct" is, I think, a fundamentally
impossible task.  The music roll police will not be knocking at your
door if you're off by a few percent of what the label says.

Roger Wiegand - Sheltering in place in
Wayland, Massachusetts