Print to Fillable form or Overlay PDF's?

Yes. Start with the form you have that you want to overlay form fields to. From a new blank document, add your form as a background. Then add in all of the form fields you want. Remove the background. Now you have a document that is just the form fields. Save that document.

Now each time you want to fill out that form, open the form field document, then open your form as a background. Fill in the form fields and then print to PDF to get a filled in PDF.

This doesn't appear to work in Acrobat DC.

I created two documents.  One is the scan of the paper form and the other document is a blank page with form fields and checkboxes.  I open the scanned form in Acrobat DC.  Then, on the left side, I open the Navigation Pane, select the Layers button, which opens the Layers panel, then I select the Layers menu and from there select "Import as Layer".  I then specify the file to open (the blank page with form fields), and under "Create new layer", I give the new layer the name "form overlay".  I noted that "Order" in the bottom left says "Appear in front of page".

Once that is done, the form fields are there and visible, but are not editable.  For example, I see that check boxes are added, but I cannot check/uncheck them.  If I start over and put in some initial text into the form fields of the form field document and use that as a layer, I can see that initial text and it is in the right place, but it cannot be edited.