If you already have the 3kW square wave inverter, that is the hard bit done. Can you not just filter the square wave using a big LC filter to get only the fundamental (50 or 60Hz) sinewave? The LC filter will filter out the higher order harmonics that are turning your sinewave into a square wave. You might need several LC circuits in series depending on the purity of the sinewave you need
Forget about using a huge, expensive and lossy LC filter on your squarewave inverter. Its voltage is too low since a sinewave has peak voltages 1.414 times (the root of 2) higher.