Hello bpphannon. Speaking if I may as a plant pathologist. I have to admit, soil steralzing is not to my taste. Due to the fact that it entails a process much like baking the soil. Yes! this will kill practically everything, seeds bugs and disease. You are then left with a quantity of dead soil.
You say that you have lots of bagged soil and are attempting to cleanse it, via riddling/screening. Using this method, perhaps a really good helper is to identify roots etc in the soil. At the same time having some knowledge of of what root produces what plant.
Perennial weeds such as nettles, dock, and bindweed really need taking out. Nettles for instance are a valuable medicinal plant. The roots will be very woody in appearance and usually entangled. Actually soil that has been home for nettles is very rich in several nutrtents. The colour of the roots is a reddish brown. Then the dreaded convulvous or bindweed. These roots are white and like spagghetti and can grow on and on. Docks are very woody-like. Thin perhaps even masses of fiberous roots usually are annuals etc.
My general practice here is to, ok, search for the obvious but a much easier route is. Tip the bags out, spread the soil about a bit and let the weather do the rest. As the perennial badies appear, root them out. most seedings will be annuals etc.