You cannot do what you describe because the Variax is not capable of using two different models simultaneously.  The JTV series, however, is capable of sending 2 different outputs simultaneously using both a Variax model over the VDI interface and the output of its magnetic pickups over the analog output. The JTV-59 (whose mangetic pickups most closely resemble a Les Paul) might be your best bet to get the gibson tone. Use a Variax acoustic model as well.