So as not to confuse the issue, I thought I'd lay things out in a more orderly manner.
This book is built using Sigil for Mac, the font in Sigil's BookView is "Times New Roman" and I created the italics/bold both by using the buttons on the Bookview and by adding the tags manually in the CodeView.
This is the code view:
This is the paragraph in Sigil's BookView:
This is the paragraph in Calibre:
And this is the paragraph in Readium:
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As for the whole <span> idea that I mentioned earlier, that was just something I thought of from my frustration as a possible work-around -- that wasn't how I actually do italics, etc.