Can you recommend an efficient encoding algorithm for sound with long periods of silence?
Thresholding should reduce the file size to the limits of the encoder being used. AAC/H.264 are using the state of the art general purpose audio compression codecs (which could only be beaten by application specific optimized codecs, such as speech vocoders etc).

May be your files are already minimal? Put some numerical data such as the sampling rate, average bits per sample, recording duration and file sizes...