Please try to use rtsp publish. Rtsp doesn't require 44100 audio so you don't have to transcode audio.
ffmpeg command will look like
ffmpeg -re -i htttp://yourhost.com/live/stream/playlist.m3u8 -c copy -f rtsp -rtsp_transport tcp rtsp://127.0.0.1:7554/live/stream
rtsp -rtsp_transport tcp require to force using TCP. TCP is more reliable to should be considered for such cases.
To use RTSP you:
1) need to setup rtsp inteface as described here
http://blog.wmspanel.com/2015/05/rtsp-transmux-hls-rtmp-dash-mpeg2ts.html
2) please do that carefully. and don't switch current production streams. create new stream for tests first
3) recommended ffmpeg versions are 2.8.x. Rtsp works strange with 2.5.* sometimes