The greater the distance, the more the signal is attenuated, so the harder it becomes to distinguish signal from background-noise, so the slower you have to send.
'Modulate the light from our star':
Not sure how one might set about that. As things stand, we need extremely sensitive instruments to detect the starlight-modulation caused by orbiting exoplanets. A planetary-scale modulator would give you a bandwidth in the order of one bit per orbit.
Supposing we could construct a device that could modulate sunlight, it would need to be big - orders of magnitude bigger than anything humans have ever made. Our interstallar probe would have to deploy such a device on arrival, in order to 'call home'.
I suppose it's conceivable, as an idea; but the cost of such a project would be unimaginable, and the benefit would be useless information: e.g. "There is life on this planet; but you have no chance of getting here, and they have no chance of getting to you". That's not actionable information.
And you'll be getting the signal 20,000 years after launching the probe; that's the span of all of human civilisation. There's every chance that humans 20,000 years in the future would not be very interested in a signal from a probe launched by their 'primitive' ancestors. That's if they had any cultural memory from their ancestors that there ever was such a probe; but how much do we know about the culture of humans 20,000 years ago? If they had launched a probe, we would have to learn that from fossilised bones, which seems far-fetched.
Oh, my goodness. Hyperbole much?
Detecting signs of life is all very well; but most (all?) such signals will have come from so far away that either we'll have evolved, or they'll have evolved. The chances that we'll ever meet such beings is minute.
I would expect the greatest discovery ever to actually make practical difference to something.
The tiny bandwidth and enormous turnaround time for any electromagnetic signal over (say) 20LY will stymie any attempt to transfer useful amounts of information. Probes are more promising; but note that Voyager 1 has travelled just over 1/1,000 of a light-year so far. To travel 20LY, it would need to survive in deep space for 40,000 years. Humans have never built a machine that could survive in working order for more than about 200 years.
For such a probe to tell us anything interesting, we'd be faced again with the bandwidth problem; or the probe would have to come back. By the time we got information back, it would be 40,000 years in the future. We know barely anything about human culture 40,000 years ago; if we had launched an interstellar probe 40,000 years ago, we'd have zero cultural memory of that fact by now.
So this "greatest discovery" is most likely to fall into the "gosh, that's quite interesting" category, rather than the "most important ever" category.