Welcome, Christian, to the small circle of Piano Melodico owners!
We will not discuss whether restoring these instruments drives one
crazy, or whether you were already insane to acquire the thing in the
first place :-)  But the musical performance can be quite good once
everything is right.

I have a 30-note instrument that is complete and mostly working.  The
"piano" control works by placing a felt-covered bar over the backs of
the hammers, to limit their travel distance on the backswing.

Your hammers should all have a felt covering on their shanks, part way
down from the heads, which serves no purpose unless the "piano" bar is
engaged.  The bar is actually a thin plank, hinged from the top edge so
it can be pivoted in or out of the way of the hammers.

By the way, mine uses a small draw knob (like an old organ stop) to
control the piano bar.  It has no markings; you must watch and listen
and figure it out yourself.

A second knob engages the honky-tonk (lute, zither) tabs, which I
expect are very difficult to restore and get adjusted right (there is
a good reason why hardly any grand pianos have the "honky-tonk" system
found in many uprights.)  On the P.M. these tabs are of leather, which
slide over the strings where the hammers strike.  If the leathers are
too old and stiff, or too new and soft, they won't work right.

A third control raises the dampers, just like in a manual piano.  Not
all models of the 30-note P.M. had all three of these features, or so
Bowers' Encyclopedia seems to imply.  So your piano might have not had
all three items.  Personally, I think the damper control is of little
musical value.

Good luck with your restoration.  The instrument is really quite well
built, but it sounds as if yours was badly stored for many years.

Mike Knudsen