Hi Colby,
Optimal spacing? If I recall correctly, Beyfuss said something like 4 or 5 per square foot (don't hold me to that though...just from memory). Lots of folks like 6x6 and more like 8x8 or more. The more I deal with and observe ginseng, the more I question some of the traditional wisdom. For instance, we all know that the closer together plants are the more likely they are to get a disease, and for that disease to spread wildly before we can get it controlled. In a wild sim planting, we are left to watch. For this reason, many have gone the route of planting farther apart.
To be honest, I don't play that much attention to the spacing when I'm planting with the seeder. I step into the area to plant, then start on one side of my body and plant, then move the seeder in an arch in front of me while still standing in the same place. I normally move sideways maybe 8-10 inches. When I"m done with that arch left to right I take a small step forward...maybe a foot. So, my spacing would average somewhere in the neighborhood of 8x12 or so. However, I often plant more than one seed per hole.
I think the ECF seeder will help with your weed issues...particularly garlic mustard. Since it doesn't disturb the soil around the hole, it does not bring seeds from the soil up into the light where they can germinate.
Of course, I dont consider the plants you mention to be weeds! lol