Id do a combination of things.
A frame chicken tractors
AND the 5 gallon buckets to be sure you can get the birds as close to the plants as you can without them being able to damage them. Maybe a large rock on top of the bucket too so it doesn't get knocked over and expose the daylilies to ravenous chickens? Seriously I'd get some CX and limit their food and force them to graze eating down the weeds you don't want and your getting free range organic fed chicken. Cuts down feed costs for the CX. Its a win-win situation. Or get 25 sex link cockerels and throw them in there. You know those are all boys, and they are about as cheap as anything I've seen coming out of the hatcheries. Get them started, put them in the tractors in the spring and when they are ready to make you pull your hair out from the crowing and the fighting, send them to freezer camp. By that time the seasons close to being over and your getting ready for a nice Mass. winter. Imagine the stock you'd make from that batch of cockerels?
Id put a 5 gallon bucket with a hose to a nipple so they can drink on top of the tractor too. That way your not hauling water daily. When the season is over you put it away till next year and order another batch of freezer camp invitees.
Maybe you do both CX and some sex links. Divide up an order so you have immediate birds ready to hit the ground and the sex links that take longer but are out there longer. Plus you'd have them scratching the beds up and manure back into the bed. Pull some for your horses too. But it saves on having to totally eradicate it by hand from your garden beds and using chemicals your not happy about using.
I'd treat it like the renewable resource that it is and I'm dead serious. Your goal is to keep it down not totally gone. I bet that's why the early settlers brought it with them. Super tough and super easy to grow and the livestock love it. I'd bring it with me too.