Here is a really cheap solution. Buy the disposable ziplock/rubbermaid "tupperware" and cut a hole in the top with a utility knife. If you don't over fill it they can't scratch it out all over the place. Also, it will hold plenty of food for 3 chicks and doesn't take up a lot of room in the brooder. Worked perfect for me!
I do this also and use anything handy like soft butter tubs or plastic shoe boxes from the dollar store. But I put rocks and sand in the bottom to weigh the container down. Believe me they will try to overturn it to scratch the contents, and the sand provides them with the grit they need if they ingest the bedding.
When the chicks get to where they can jump the taller the better so they don't throw their bedding into the food. Those little feeders sold at the TSC are worthless unless mounted on top of something. They are so light the chicks easily tip them over and the rubbermaid and butter tubs are so much cheaper.
Same problem with water too, unless stacked on top of bricks the water dispenser get filthy in seconds making it a constant battle to keep clean water. I again use the same tubs filled half way or more with rocks. Yes I have to rinse and fill them twice a day. But it is much less than the 5 or 6 times a day trying to keep the TSC quart water dispensers clean.
I have one of those red plastic rectangular feeders. I screwed the bottom of it to the flat side of a 2x4 as soon as they could reach, maybe a week old. Now they are almost 7 weeks and it is still working well as the second feeder, for the ones who get bullied away from the big one. Waterers I just set on bricks or something -- if the waterer is set on something big enough for them to stand on, the water stays clean longer (well, half a day....)
mine do a similar thing, but luckily not a huge pile of food in the brooder *yet*. but I plan to raise it today seeing as they are growing by the hour and are getting so big.
I have a silkie chick that is really small, but she seems to make the biggest mess. I have one of the round chickfeeders with the holes on top and she fits in the hole so she stands up there and tries to see how far she can send food flying.
The bigger chicks stand back out of the way. Cracks me up!
Each day, we just dump the food out of the pan and back into the feeder. It's saved us a LOT of feed. The peeps are almost five weeks old now, and they aren't doing it nearly as bad as they did for the first few weeks.