I determined the issue (and updated the thread title to reflect this): The table I'm copying contains some merged cells. I do get two warning messages about the merged cells (see screenshot at bottom), which I've been ignoring because the merged cells copy over flawlessly (in spite of the messages). Nevertheless, even though the formulas are not in the merged cells, and the merged cells copy over without issue, the mere presence of the merged cells interferes with the operation of Paste Special ⇒ Values and Source Formatting, preventing it from converting formulas to values.
The fix is thus to do two copy-paste operations: One for the rows containing the formulas, and one for the row containing the merged cells.
Note: The reason I don't see the warning messages when I instead do Paste Special ⇒ Values and Number Formatting is because this operation doesn't preserve the merged cells. And since the merged formatting is destroyed, the formulas are properly converted to values.
Essentially, when merged cells are present in the source, Excel treats Paste Special ⇒ Values and Source Formatting as a normal paste operation.