It appears that generally the paragraphs that should be in the row above are formatted with no space above. If we use that as the trigger to move the content up then these changes to the macro might get you most of the way there. There is at least one case where the conversion didn't add a paragraph mark so that might need a manual fix
Code:
Sub FixTable2()
Dim r As Long, c As Long, RngSrc As Range, RngTgt As Range, aCell As Cell
With ActiveDocument.Tables(1)
For r = 3 To .Rows.Count
For Each aCell In .Rows(r).Cells
If aCell.Range.Characters(1) = vbCr Then aCell.Range.Characters(1).Delete
If aCell.Range.Paragraphs(1).SpaceBefore = 0 And aCell.Range.Paragraphs.Count > 1 Then
Set RngSrc = aCell.Range.Paragraphs(1).Range
RngSrc.MoveEnd Unit:=wdCharacter, Count:=-1
RngSrc.Select
Set RngTgt = .Cell(r - 1, aCell.ColumnIndex).Range
RngTgt.MoveEnd Unit:=wdCharacter, Count:=-1
RngTgt.InsertAfter vbCr & RngSrc.Text
aCell.Range.Paragraphs(1).Range.Delete
End If
Next aCell
Next
.Rows.HeightRule = wdRowHeightAuto
.Range.Paragraphs.LeftIndent = 0
.Range.Paragraphs.RightIndent = 0
.Range.Paragraphs.FirstLineIndent = 0
End With
End Sub
Does this version get you closer to the desired target?