Interesting analysis - in particular that you've come up with a figure of 100mW per square meter, which is two orders of magnitude less than most of the other postings assume.
You don't make any mention of moving the beam around - surely that would cut power requirements? Signal one 1,000Km stretch of coast for a few seconds, then the next, etc, then return. Maybe enough to knock another order of magnitude off the sums?
Which brings your final figure down to 2.3MW (for the Indonesia case, admittedly). Too high for direct power from (reasonable sized) solar panels, but surely the satellite would have some sort of stored energy system; flywheels or capacitors. Would reduce the allowable duty cycle further, but really only need a bright flash every few seconds.
To answer your other point: if the satellite happens to be in front of the sun's disc (or even close) you obviously won't see it. But you're going to need a few of these things for coverage anyhow, even in geostationary orbit.