As Nick alluded to, installing the rigid plastic strips were easier before the bottom was hog ringed in place. I didn't have to remove the rubber bottom to do this. Because there were 3 holes in the strips, I opted to use the zip ties and stainless steel washers as well, as I figured they will help anchor the strips in place and fill in the holes in the seat bottom.

Before:
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I applied leather conditioner before and during the pulling and stretching process:
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Here is the underside right side bottom cushion finished:

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After:
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This was my first attempt at upholstery work, so I took my time to try to install the skin properly, and I was pleased at how well it fit.

The upper half is next...