RE: Making large sheets of balsa help please
Use 1/16" ply as a doubler. Just as strong and much thinner. Glue it together with aliphatic wood glue (Moo Glue!). You might consider using the lite ply as the forward section of the fuse side.
As to the lamination; one lenght of 4" and one of 3", tape one side and use the MooGlue. Could be watered down just a tad. Of course both edges should be square in length as well as edge to edge.
The 1/16" splice is used all the time in large built up sailplanes as is the lite ply forward section.