The problem is your ffmpeg. If telling ffmpeg to use aac causes it to encode in he aac, if that is true, then there is something wrong with your ffmpeg, because specifying aac should never result in he aac. Only telling ffmpeg to encode using libaacplus or libfdk_aac should result in he aac encodes.
Here's an idea... build your own ffmpeg from source, because your binary was built wrong (if what you are saying is true).
You can download the ffmpeg source and build it manually:
git clone git://source.ffmpeg.org/ffmpeg.git ffmpeg
But its far easier to install it using package management, like macports:
MacPorts requires an appropriate version of xcode; xcode_5.1.1.dmg is the most recent version for Mavericks (after registerring for a free developer account, and logging into developer.apple.com, that link will begin your xcode download). Once the download completes, open your Terminal.app and complete the installation:
hdiutil attach -quiet -noverify -nobrowse -noautoopen ~/Downloads/xcode_5.1.1.dmg
cp -npR /Volumes/Xcode/Xcode.app /Applications/
hdiutil detach -quiet /Volumes/Xcode
Download and build macports:
MacPorts Guide
curl -Ok https://distfiles.macports.org/MacPorts/MacPorts-2.2.1.tar.bz2
tar xf MacPorts-2.2.1.tar.bz2
cd MacPorts-2.2.1
./configure
make
sudo make install # *not war!*
cd ..
rm -rf Macports-*
sudo /opt/local/bin/port -v selfupdate
diskutil quiet repairPermissions /
add macports to your $PATH:
export PATH=/opt/local/bin:/opt/local/sbin:$PATH
export MANPATH=/opt/local/share/man:$MANPATH
build your ffmpeg
sudo port -vsc install ffmpeg
you can keep everything updated simply with:
sudo port -vsc selfupdate
sudo port -vsc upgrade installed
If you are unsatisfied and/or need to remove MacPorts:
sudo port -dfp uninstall --follow-dependencies installed
sudo port -dfp uninstall all
sudo rm -rf /opt/local
sudo rm -rf /Library/Tcl/macports*