I don't think it would be a matter of modifying it but completely 
redesigning it.

You might want to look inside a Bolex camera to see an example of how a 
variable shutter works.  The Bolex has two sets of shutter leaves and a 
gadget that pulls them apart as a ring is moved forward and back on the
shaft.  This works well, but it's not a thing you could easily fabricate
into an existing projector.

If I were doing it, I would toss the existing projector entirely and I
would build an electronic projector from the bottom up along the lines of
the Kinoton projectors.  The Kinoton has stepper motors driving the two
sprockets and a stepper motor driving the shutter, and they are all
controlled by a small microcontroller.  You could do something similar
using an existing junk projector chassis and add a second shutter.  It
would be fairly easy for software in the microcontroller to change the
shutter phase.

It would seem much easier to do this than to try and implement a variable
pitch shutter entirely mechanically, and it would also make speed control
a whole lot easier.
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