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I ended up simmering the zest of 6 oranges (peeled with a vegetable peeler, so there was still a small amount of pith) without rinsing at all. When they were tender, I added the supremed segments of those oranges and simmered the everything for another half hour. I strained the syrup and gave the solids a bit of a whir in the food processor.
I have just enough puree for one more cake, and this lovely orange syrup. I used a lot of sugar. I can't guesstimate how much sugar because I just kept adding it until I got the level of sweetness I want, but the viscosity of the strained syrup is like Aunt Jemima pancake syrup.
I'll bake the cake again in 3 or 4 weeks. Will the puree and syrup last that long in the fridge? Or should I freeze it?