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Thanks for that.
The odd thing is that when the figures were embedded in the text, rather than all put together at the end, that syntax (error) for \singlespacing{\caption{...}} didn't matter---caption still stepped up the counter. Only when the figures were bunched at the end did it matter.
But ...

After several hours of trial and error, I discovered that when the figures are in a separate file (input at the end of the document) or just moved to the end of the document, the \singlespacing to control the layout of the \caption matters.
Removing that got the referencing right. Though at the ...

I have a paper of about 35 pages. It has about 8 figures, which while writing, I embed in the text. For submission the journal wants me to put the figures on separate pages at the end of the text.
When the figures are embedded in the text, the numbering and referencing is correct. When I simply move ...