If your shield is smaller than the star's diameter, you have a penumbra effect. Rather than stellar occlusion, at a sufficient distance you have a stellar transit.

Building a static support for your polariser might also prove challenging.

Ah, yes of course. Though if your disc is large enough, such a transit should still be detectable.

You're trying to detect the modulation, not merely the transit.

Your noise floor is now vastly greater.

They could be basically the same - during each transit you could either let the light through or block it.

Now you've decreased bandwidth to orbital period.

I missed the part about some minimum speed, but it's still flexible in regards to how many levels or frames per transit you use. The point is really to be able to communicate at all - without using a star's light it's basically impossible after a certain distance.

There is that "something is better than nothing" element.

I've also been thinking of whether or not some sort of stellar laser or maser might be possible. Modulating a narrow, tightly focused beam.