I readily confess I know very little about streaming, presently. But I am interested in your problem because ultimately I would like to try some streaming. Let me begin with a few basic questions. Are you streaming H.264 or AVC (H.265)? What other settings are you able to adjust on the stream when you set it up? For example, is this a CBR or VBR stream?
And you mention that you cannot go higher then 6 mbs. What is the limiting factor when you attempt to stream higher?