As you know I've been a ham most my life, and I figure you were talking to the readers as well, but totally understand and agree.
The biggest flaw I see is this though:
Let's say we send a signal and 45,000 years later by some miracle it is intercepted. Although we send coordinates that should greatly assist "Others" to find us, by time they receive the transmission, we have moved within the solar system, it has moved within the galaxy and it has moved within the Universe - in the big picture of how far everything has moved it could be billions of trillions of miles and EVERYTHING shuffled like a deck of cards made up of billions of cards.
We can say (and correctly so) that the Mayans have nailed the time it takes our solar system to orbit within out small and somewhat random looking galaxy, it is true a hundred billion stars is at best an average, even a little smaller than average galaxy, so nothing much about the Milky Way stands out.
But Mayans figured out that we orbit within the Milky Way every 25,000 years or so, and predict from a random start date that December 21, 2012 will be the date we return to that start point. It does go greater in that our positioning with the other galaxies and the known universe (which grows by billions of years every time Hubble gets a new pair of glasses) but our galaxy's alignment does have notable alignment with the Current center of the Universe. Of course, how do we know where the center is, if we don't know the Universe's boundaries, if indeed there are any.
Which brings me to my simple but EXACT solstice calendar I have mentioned before - on April 15th (tax day was as good a day to remember as any) I marked the time the sun cast a shadow on a seam on my living room wall's wallpaper - it is 7:31am. The time and date are of no relevance, only that you have a fixed spot to use as a time-line. It could have been any number of minutes earlier or later, or on any date, but the important part is that using a fixed spot allows you to await a year to go by and miraculously the sun is EXACTLY where it was the year before and to the minute. If literally was 4 inches short the day before and 4 inches beyond the day after the 15th at 7:31am, but on the 15th, I sat watching it crawl across my wall and like a Swiss Watch strike the seam exactly as it did a year earlier. Lastly, no other day of the year will it align at that time, there is no 6 month repeat of the event, it is a one shot a year thing.
Now... if I hadn't read the information needed to create my own solstice calendar, I would NEVER in my life time know how long a year was if it wasn't already known. I'm amazed at the people who figure out such things and how distant in the past (literally 10 thousand years ago or longer) and that really blows me away, considering how short a time ago it was that we still thought the world was flat, even though during eclipses we see Earth's shadow move across the moon and of course appear round, rightfully so. I know much of the flat Earth theory was "church" forced concepts and event though the moon appears round, doesn't mean it is a sphere, indeed for all we knew in more ancient times, it could have been flat as a coin.
Back on track though, we will NEVER be able to find anyone "out there" it is up to them to be capable of finding us. If at best all we can do is send radio signals across the spectrum, we are mere cave people feeding off the marrow of animals that other animals took down. We've only figured how to smash bones with rocks, and I doubt this over-populated planet stands a chance to ever survive long enough to go to the stars.