Most of these treatments will work best in late spring, when these weeds are growing fastest. Because they work best in quickly growing plants, if you feel it necessary to begin treatment this fall, mow the field high (6-8"), and then treat the regrowth before it matures. Dock has a very deep, resilient taproot, and more than one application may be necessary. Also keep in mind that the ground is probably a decently loaded seed bank for the stuff by now, and you may have to deal with seedlings for years (although after the initial control, it won't be as bad).
So to answer your questions...
- What chemical would be most effective?
I'd definitely say I'd have to choose a 2,4-D/Clopyralid mixture (in a ratio of about 8/1 respectively). These are both auxin mimicking chemicals, which together will be extremely powerful against the weeds, without really upping the chemical dose, or really harming the grasses, which don't respond to the broadleaf auxin mimics. As I said, though, with Dock, more than one application may be necessary (Most likely application 2 will finish off anything left).
You (obviously) need a pesticide applicator's licence to apply these chemicals, but they are both legal for residential use in most U.S. localities. Make sure you add a decent amount of surfactant to the mix, as dock tends to shed water droplets easily. Use ~4 quarts per acre.
- When and how often should that chemical be applied?
You want to apply it when the plants are actively growing and the faster the better. This is because of the mode of action (auxin mimick). Mowing off most of the leaf surface will cause regrowth, which will be far more susceptible than matured plants. A heavy nitrogen fertilizer will actually make this effect more pronounced, and you get better control.
Within a week of application, the weeds should start curling up. They will steadily decline to a point, at which some die, and some may slowly seem to revive. If you see any new leaf growth after the first major dieback, apply again. That usually finishes off the tough few. You may have enough time for all this before cold weather sets in.
- How should the area be prepared for this application(s)?
If the plants have ripened seedheads, it's best to wait for the next season, because coaxing out a good flush of growth will be a challenge. Other than that, if the plants are still quite green, but are simply slowed down, a high mowing will work great. In spring after the weeds go out of dormancy, you can apply any time without treatment.
And finally, is there anything we're failing to consider?
Not certain. My main concern is that Dock often grows most vigorously in damp ground, and I wouldn't recommend using any broadleaf herbicides near groundwater, or in an area that drains directly into a water body. These chemicals tend to be mobile, because they do not bind to soil and can have a persistent half-life. You should be good, though, if this is a normally drained area, away from any creeks, etc.