I recently had a similar conversion of a Stagea rear diff into a R32 GTS4. Basically what I had done was to take the crown wheel and pinion out of the Stagea diff, and have the C/W attached to the R32's viscous centre and both bits replaced into the R32's diff housing. (That's not exactly what I wanted - I wanted the whole centre transferred, but that's a different story!)
If you simply replace your GTS's diff centre with the new mech LSD centre, everything else should be re-useable, including the output shafts (so you retain the bolt patterns of the GTS).