Let's see, Greensand is 4% P, Alfalfa 2% P. Never seen greensand at the local feedmill, fertilizer wholesaler etc, although can't say I was looking for it either.
Alfalfa pellets are CHEAP @ about $6.00 per 50lb, I can buy down the street and if you have ever used would know what beautiful turf results from its use. You can try to get scientific about this whole thing but I have found by simply using Organics and a little forethought, leaving the clippings and using good cultural practices that nature takes care of the details. Frankly I could give a rats azz about your sites recommendation. Grass is really easy to grow , it really is.