I wouldn't recommend using CCs and legacy form fields in the same document. They achieve the form functionality in different ways. Legacy form fields require the form to be protected for forms. CCs do not and as Andrew has suggested, do not provide the tabbed access when so protected.They provide that when Editors are applied and the document is protected as read only.
You can however bookmark the content control and you can lock the control against deletion. My CC Tools add-in
Insert Content Control Add-In has a module to convert legacy form fields to rich text controls retaining the bookmark names (though the controls themselves are not bookmarked).
The bookmarking can be achieved easily enough with a simple macro. (Macro1 below). You can then use the option to add editors and protect the form. Test the outcome with Macro2. This will write the same value to all the controls. If you are happy with the result, you can clear the test values with macro3.
You will need the form password, if any, to convert form fields to content controls.
Frankly content controls are rather more robust than legacy form fields and if your third party application will work with them when bookrmarked (if it just writes to named bookmarks, it almost certainly should) that would be the way to go.
I suggest you experiment with a copy of the form.
Code:
Sub Macro1()
Dim oCC As ContentControl
For Each oCC In ActiveDocument.ContentControls
oCC.Range.Bookmarks.Add oCC.Title
Next oCC
Set oCC = Nothing
End Sub
Sub Macro2()
Dim i As Integer
Dim sName As String
Dim oBM As Bookmark
For i = 1 To ActiveDocument.Bookmarks.Count
sName = ActiveDocument.Bookmarks(i).Name
FillBM sName, "This is a test"
Next i
End Sub
Sub Macro3()
Dim oCC As ContentControl
For Each oCC In ActiveDocument.ContentControls
oCC.Range.Text = ""
Next oCC
Set oCC = Nothing
End Sub
Public Sub FillBM(strbmName As String, strValue As String)
'Graham Mayor - https://www.gmayor.com
Dim oRng As Range
With ActiveDocument
On Error GoTo lbl_Exit
If .Bookmarks.Exists(strbmName) = True Then
Set oRng = .Bookmarks(strbmName).Range
oRng.Text = strValue
oRng.Bookmarks.Add strbmName
End If
End With
lbl_Exit:
Set oRng = Nothing
Exit Sub
End Sub