Somewhere around Season 2 or 3 of SG-1, I noticed Earth's Point of Origin on an off-world gate. Normally, this would be considered a goof, due to a limited number of props Stargates - but in this particular scene, they zoomed the camera in so close that only 3-4 glyphs were visible at once, the pyramid point of origin being one of them.
At this point, I started thinking about a new Point of Origin theory, that seems to have been partially confirmed with Stargate Universe, possibly in an attempt by the writers to "fix" the prop goofs from SG-1:
In Stargate Universe's series premiere,
on the first attempt to dial Destiny, the final chevron that would not lock was the Orion constellation. The closest star in the Orion constellation is, according to Wikipedia, 17.51 light years away. A bit earlier in the episode, Rush said they were heading to a planet 21 light years away.
With that small coincidence, it seems that the Icarus planet was closest to the Orion constellation, of all the constellations depicted on the Stargates (Or, rather, the gate was moved there from a planet in/near that constellation. I don't think that planet was originally part of the Gate network). That is why its point of origin was Orion, a symbol that is pretty common across the Stargate network.
Earth's point of origin, the pyramid on the Alpha gate we're so familiar with, I believe was originally on a planet near a pyramid constellation, before Ra took it and planted it on Earth. Then, during the next correlative update, it became associated with the Ancient point of origin, the one from the Beta gate, that the Destiny address was supposed to be dialed from.
So the Point of Origin would then be a rough "I'm in this area of the galaxy" symbol, and the particular ones used on the Stargates were meant to signify where the Ancients intended each Stargate to be positioned.
This then explains why Eli's suggestion actually worked, when any such Ancient limitation requiring a specific point of origin should have required the Beta Gate's point of origin: During the correlative update, back when Ra dropped the Alpha Gate here, those two points of origin became associated with each other. If the Beta Gate glyph was on the Icarus Stargate, that would have also worked - but because that gate was where the Ancients first settled, that glyph was truly unique.
Oddly enough, this also works with the original Stargate movie. Daniel Jackson needed the point of origin for Abydos, but according to the commonly accepted theory that the point of origin is unique to each and every gate, it should have been simple to determine. Excet he only knew what it was once Sha're showed it to him, meaning either there were a few differences between the Abydonian gate and Earth's gate, or they were completely identical - point of origin symbols and all.