Have you tried sorted the images on Lightroom web.
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Try changing the Collection settings to Custom Order. You may have it set to capture time. In LR desktop go to the Collection and click the drop-down icon to change. When a collection sort is set to Custom you can drag the images around and they should always stay in fixed positions.
This pointed me to the correct fix — but it also raises questions. I had sorted by name, as the page spreads are named sequentially and that was the easies way to make sure they are in the correct order. However, upon reading your reply I see that the web version of Lightroom does not offer name sorting as a choice, only date and custom — and this must somehow carryover to the web view. I went back and made a custom sort in the correct order and that seems to have transferred correctly to the web. Thanks for your help. And Adobe should allow sorting by name to be included for the web. Just saying!