We have virtually zero forage this time of year. By May, my feed consumption per bird will drop in half.
While trying to get grass to grow, chickens will benefit more from tender forbs like clover, alfalfa, forage type turnips, radish, etc. They are more nutritious for monogastric animals and less fibrous than grass.
If you use a proper feeder, you'll cut your feed bill even more. If fermenting feed, you'll cut the bill in half from what you achieve dumping dry feed on the ground.
Check the type of feeder I posted below.
When the crop is empty, that is the hunger signal and when they will mob you. The crops are usually empty in the morning and they want to eat as soon as they wake up.
What type of feeder are you using for the chickens now? When you say dump the feed, do you mean on the ground?
This is my favorite chicken feeder for eliminating and ease of cleaning. It may not work for ducks though.
https://www.tractorsupply.com/tsc/product/harris-farms-hanging-feeder-10-lb-capacity
The baffles prevent the chickens from billing the feed out.
I run through about 20 pounds of feed a week for every 10 birds but that varies dramatically from season to season and whether I feed dry or fermented.
Hay isn't a good idea for chickens. It much too fibrous for an animal without the ability to chew.