Leather V-belts have become pretty much obsolete, for good reason.
The old ones might have been made out of better leather, so it is not
fair to compare them to new ones, but any original belt is going to
be either rotted or dried out unless it was treated regularly with
a suitable conditioner. Modern laminated rubber belts are vastly
superior to any leather belts you can find today.
The reason four belts were needed on the steamboat pump is because
even the old [better?] leather belts worked so badly. Unfortunately,
it is difficult to find rubber belts today that are carefully made
and that will run quietly in a piano. This is one of the reasons that
many people locate the pump remotely. However, it is possible to find
decent belts, although they might be fine from one manufacturer for
a while and then in later production they will get lumpy and noisy.
Dayco fractional horsepower belts were great for a while and then they
got sloppy and noisy.
I prefer custom-made belts of urethane because they can be totally
silent if carefully made. They have their issues, such as stretching
initially, so you have to be willing to experiment a little to get the
size tight, but urethane will last a long time and be totally silent if
you get it right.
The other problem with urethane belts is that the most common color is
bright orange, which looks really awful in a piano! Urethane does come
in black but fewer places stock it, so you may have to get a roll and
make your own. I believe McMaster-Carr will make belts to order and
they may stock black, but you may have to try a few times until you get
the length right.
I have a roll of the orange stuff and the tool for splicing it, in case
anyone wants to try it.