I don't have a workaround for you but I can tell you why. It might help you figure it out for yourself. The soundfile in an .avi can either be Constant bitrate (CBR) or Variable bitrate (VBR). When you say sound is in sync at the beginning it has something to do with (VBR). In some programs you can choose whether you want (CBR) or (VBR). I have never tried 3 GP converter myself. Maybe someone else here has and can tell you more about the settings. I know that using VirtualDub MOD you can set the delay when interlazing audio and video, but don't know what format you make it into, thus I don't know if it will work for you.

Hope this helped a little