InfoPath Dev

I converted an existing InfoPath form to FV and continue to use the InfoPath-created document library. I added a new field (Start Date) to the FV template and promoted it, but when I update my FV template, the new field/column is not available in my document library. I think I can add the field to the existing InfoPath form and publish it, but I'm not sure that the FV template will recognize the InfoPath promoted field even if I create everything exactly the same as I did in the FV template. I'm sure there is a way that FV forms are created from scratch and have a related document library, but I haven't done that yet as I work to convert existing forms/document libraries to FV. My Submit button points to a particular SP document library. By the way, we are on-prem.

You should be able to just publish the same form you use in FormsViewer to the library to promote your property. Or download the current form from the library, add the promoted property and republish it.

So, I would open the FV template in design and publish directly to the document library instead of using Manage Templates in FormsViewer. Correct?

Yes. Personally, I would save the currently published form from the form library first, just in case I needed to republish that....