I can help with this. First, the port feeders and roosters, well they don't do well together nor does any hen enjoy having to stick her head down into a pipe elbow to eat while blind to predators. They do work for hens and there is a place for a plastic feeder before rats and mice show up, then they become rodent feeders.
The engineering of making a constrained/funnel shaped box of feed dumping out onto a flat pan would work IF you sized the throat of the box just right or made it adjustable. Between 5/8" of an inch and 1" of opening, the feed will flow out on a flat surface and stop once enough feed has piled up on an angled surface, you will need more for a flat surface, simple friction of the feed piling up on the surface versus the weight of the feed in the feed bin, and the amount of friction the feed has flowing through the throat of the device will balance out. In engineering this is called the angle or repose when calculating the size of a pile of loose materials
Say you took a five gallon bucket of feed, hung it from the ceiling or a bracket, used a 4" pvc pipe coming out of the bottom of the bucket, dumping onto a flat surface/tray and adjust the height. I would make the 4" pvc pipe longer than say 6" so the rooster could get in to get to the feed without feeding blind (side eyes = prey species, super paranoid for good reasons). Then experiment with the length of the pipe or raise or lower the feed bucket until the feed flows as you need it to flow. Now you have what you wanted, a feeder that roosters can use safely.
What you also have is a rodent and wild bird feeder and a pile of feed that hens would love to rake through if the feed is not a consistent pellet or crumble, looking for treats. As long as you have a very tight coop, no gap over the size of a nickle, and don't use free range this sort of feeder would be cheap to make. The feed waste though would be a constant cost forever more.
While it is not impossible for a rooster to damage their comb on the edge of a metal feeder, the feeder sides should have been seamed, folded over to provide a safe edge, or a clip of U shaped folded sheet metal installed over the cut edge to make them safe. And having a wide door that swings in instead of up is a lot safer, most chickens will eat from the center of a feeder IF you block side access with a couple of concrete blocks or a couple of milk jugs of dirt.
Good question. Love to see an open mind asking questions.