Your first photo makes it appear that there may be a joint between the
slotted barrel and the larger portion. Is there?

Nope, it's a single cast piece, no joints.

I'm assuming the part is the moving section of a valve which modulates an
air flow to produce the loud 180 Hz acoustic waveform emitted by the fog
horn

That is correct.

Do you know how those slots were originally made? You could probably tell
from the finish of their walls whether they were cast around fins on the
core or cut with some sort of saw or milling cutter. I'll wager they were
cut though, they look pretty thin for any reasonable core material of
their original era.

On the very oldest samples of these horns, the piston's slots are
lathed, and only the 6 inner ribs hold the rest together. On the newer
style pistons (1930's on) as seen in my photos, the slots do not go all
the way around and they are cut on a mill with a circular cutter.

Cutting those slots will require some kind of milling or rotary saw setup,
along with fixturing to hold and position the part in the correct location
for each slot. I suspect they have to be located axially to within maybe
ten thousandths of an inch of their design locations to keep the valving
action optimal.

Actually, the diaphone gets its rich-in-harmonics tone from the piston's
slots aligning with the outer cylinder's slots for only a small fraction
of the piston's stroke, producing more of a pulse waveform than the
sinusoid you would get with just enough excursion for the slots to go
completely in and out of alignment. The slots have to be spaced fairly
precisely, but slop in their width will not significantly affect the
tone and will not affect operation at all. The wide rear section of the
piston is the "motor section" that produces the back and forth movement.

I suspect those six ribs inside the part were put there there to add
strength to the piece so vibration didn't cause it to crack at those
little solid sections between the ends of the slots.

As noted earlier, the ribs were originally there so that the slots could
be cut fully around on a lathe. The shop drawings for all diaphone
pistons show this was how it is supposed to be done. For some reason,
they switched to milling the slots later in the production of these
horns, but did not change the castings (probably for cost reasons).

-Adam