I solved this problem by making a zero dish wheel. It’s not that hard if you know CAD and know of a sheetmetal shop with a CNC laser, plasma, or waterjet cutter. Draw the design of your choice in CAD (must be good quality with all vectors attached).
A CNC shop can convert your drawing to G-code and cut out your shape. I used 1/8″ carbon steel with paint but stainless would have been a better choice.
I drilled out the rivets from the original wheel and tranferred the wood parts to the new wheel.
It was labor intensive but also cheap.