Well, you kinda gotta work with the tools you have. Mine are mower, disc and sprayer. I have no plow, but I know a plow will deep till to solve problems like hard pan and a vigorous shallow weed seed bank. Given what another had posted, its conceivable that it could stir up deep, dormant seeds.
Anyway, the way I've been working things in my compromising, sub-perfect manner is what I can present to you.
Mow first. That was easy.
I'd disk next rather than spray and here is why. The weeds need to be young and growing with foliage to accept the spray. Just after mowing is not the best time to spray. If you disc first, you will kill many weeds while prompting a new recruitment of germinating weeds. You could, like me, do a second discing a week or so later to destroy these young weeds while further preparing your soil.
Spraying should be done at the time of one of the post-till new weed flushes when they are most vulnerable. Time, fuel costs and soil conditions will dictate how many tillings you can do before you spray or plant. The more you till the more you kill while also depleting the seed bank. However, some plants (fescue for instance) persist despite a few tills which is why you will spray. Roundup takes up to two weeks to complete the kill. If you till again such as when covering seeds, there is the risk of germinating more weed seeds.
Lastly, broadcast and cover. Millet won't need much to cover. I once hand cast seed onto exposed mud banks with good results. Ideally, a rainstorm would do the trick. Barring a good rain, cultipacking is good for finishing small seeds after broadcasting as would be a gentle harrow.
Japanese millet has a longer yield time than brown millet (72 days vs. 60) but is more tolerant of flooding than brown millet. So should your jap be a little late, it can still survive a while if you begin flooding. A mixture of the two will give you a prolonged millet production season and give some insurance against flooding. Sorghum is a drought resistant plant that if added to the mix might give insurance against plot failure should the millet dry, die or get covered to deeply. I would recommend you consider a mixture or Japanese millet, brown millet and sorghum.
Finally, remember it is for ducks and not production so some loss of yield is not the end of the world. You can accept some weeds, cut back on fertilizer or lime from the soil test's production farming application rate recommendations and still have birds. Have fun with your plots but don't stress over them too much.
