Thank you ^. I have come up with a workaraound that seems to accomplish what I want.
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When inserting the reference, for the “Formatting” option, choose “Show Only in Bibliography.”
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in EITHER the “Prefix” or the “Suffix” field, type exactly what you want to appear; e.g., the reference with quotation marks & the other punctuation. E.g., Schubert, “The Final Cycle of the Speeches in Acts”;
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Make sure to use ALT codes for the quotes if that’s important to you; e.g., ALT+0147 and ALT+0148 for the open & close quotes, respectively
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Click OK to insert the reference.
This seems to work. For 2nd references to reference types using quotation marks for the title (such as journal articles), it will insert the reference just as you typed it in Prefix or Suffix without adding an unwanted period.