Well I forgot the name--is it Fiesta? There is a broadleaf non-herbicide for Canada that is based on iron.
The Canada guys will be able to tell you.
Wait; I found it.
One gallon treats 1300 square feet.
Probably doesn't work too well.
My opinion for the organic-only lawns. I include (at extra cost) 10 minutes of hand weeding during each of 5 yearly treatments. I suggest add this: Extra heavy nitrogen fertilizer reduces weeds by increasing thickness, particularly if grass is well-irrigated and cut tall. But cut short if you have the tall weeds. Water less if you have the water-loving weeds.
Always seed and aerate several times per year (using a very thick type of Kentucky bluegrass, [like "Touchdown"])--the purpose is to increase the grass density and thereby fight weeds. Hopefully others will have suggestions as to what cultivar of bluegrass has the highest density.