QUOTE
The Winamp encoder is HE-AAC only
That isn't true, winamp AAC fully support LC-AAC.
Aslo you can use HE-AAC High aka High Bitrate Encoder, to force sbr to operate above 14khz you should get trasparency at higher bitrates, even HE-AAC can reach trasparency, but not needed, because only uses more processor time at decoding.