Traditional planter will get loaded up with thatch and will have problems. When you turn the soil, you turn up dormant seeds to the top. I'd spray, then mow, then disc and wait for weeds to emerge, then spray again. 2,4D is for broadleaf weeds. A combination of 2,4D and gly is nuking it. I beleive 2,4D has about a 2 week residual, it could be a bit less though.
AMS, ammonium sulfate is a fertilizer. What it does is it wakes up the weeds and allows them to intake nutrients and the herbicide faster. They say use when you start having 65 deg F days and you have some recent rain, Weed and grasses go dormant when things are dry. Also with AMS, it can open up weeds that normally block gly. Pigweed is one of them I believe.
Burning is something that is quite difficult if not impossible to do in NY. But, it'll take care of all that thatch and help with the weeds too.
Adjusting your disc depth to something on the shallow side might help the dormant weeds seeds from going too nuts. Discs with chop that thatch down too.
When stuff is really thick, mowing high, then mowing low can chop that up a bit better.
You may want to adjust that 8 row planter and/or your tractor track width so you can grow beans and have tire room to spray. I've never toyed with soybeans, but you may be able to spray them with clethodim to curb grasses down.
Whaetver weed your fighting, ID it well. Take a few pics of what you have there before you do anthing.