Ffmpeg -f v4l2

After compiling ffmpeg-custom and flashing the firmware, v4l2 is not accepted. It works perfectly well with ffmpeg-full. Is there a solution for this to work?

The problem is that my webcam needs the v4l2 support in ffmpeg-full, for firefox to play the output video requires avc, vp8 or vp9 codecs which are not in ffmpeg-full. These codecs can be enabled in ffmpeg-custom however.
In other words, my application needs the input of ffmpeg-full and the output of ffmpeg-custom.
Who knows a solution/workaround to this?