This is how I would do it. Your base unit is a circle with radius 180cm, which is approximately 10m^2.
Place one circle at the north pole. Your starting angle is 0 degrees longitude. Place a circle at the south pole, and slide it along that line of longitude until your sliding circle touches any other already-placed circle. Then "roll" the circle to the local minimum distance between its center and the north pole; whenever moving it an epsilon east or west would not allow the center to get closer, stop. Add 222.5 degrees (actually (sqrt(5)-1)*180), modulo 360. Slide in another circle. Add 222.5 degrees, modulo 360. Slide in another circle. Repeat until the circle placed at the south pole intersects an already-placed circle.
Move each center point to the nearest grid-based point at a given precision, then name them. If you stand on the named point, you should be able to touch anything using that point as its address, without moving your feet.
A 10m^2 unit cell is a very human-sized measurement, but you are correct that forcing them into an orthographic grid is pointless when the addresses are names and not numbers.
There's no way any living human could memorize the name-location mapping for all addresses, or even just all the land-based addresses. People would need to look them up in an index from a numeric coordinate, and vice versa. As such, there is no need to orient the address points to any existing coordinate system.