Sorry to hear about your frustration. Stacked coins would be like piano keys.
When I sewed my piano keys I pieced them by pairs then sewed pairs
together and so on until I got the length that I needed. Starching and
pinning helps. However you have already sewed your pieces now.
So...let's see. How far off are the stacked coins from left to right? Can
you measure that? Maybe you could rip them in the middle and again
halfway each. Then turn them so there would be less distortion.
Does that make sense?