I've managed to fix this issue for myself by overriding Strawberry to use custom avenc_aac settings.
I created a write up here: https://gist.github.com/jvgomg/38089836f8f47aa6dcf628edac0dec08
The ultimate solution would be to fix some issues with how transcoding settings work in Strawberry, and to have a build of FDK-AAC on your system. But getting avenc_aac working with higher bitrate sounds pretty good to me!