we have an older schwing that has (for lack of a better term) a flat bottom of the hopper. Its really hard to wash out, especially on longer pours. I was thinking of welding in some plates to give some slope to the center. Has anyone else done this? Looking for some suggestions...

Fill your hopper with sand. 3 or 4 5 gallon buckets will do. Spray oil on it if you can. It will crust a little and make cleanout easier. Don't weld plates in as Schwing longrocks (which is what you have) don't have wipers on them, and the concrete that loads up will prevent your rock valve from throwing properly.

My hopper is the  same way they have some plates you can buy that are formed to fit what you want to do, you may have to relocate your remixer  blades.