Improving the separation of a signal into source and filter
Have you considered using a higher order filter for your LPC analysis?  LPC analysis is known to be sensitive to the presence of noise, say additive, so it may be useful to preprocess/denoise the signal to have the best/cleanest signal going in. Are you using a microphone on a mobile device?

If those don't work, you should look into research on spectral envelope extraction, or alternative algorithms for voice-morphing.