The average should be around 6 Mbps, when you account for the buffer. The average displayed by the router will be all data read in the past 10 minutes divided by 600 seconds. If that in includes a 90 second buffer (an arbitrary for instance), the true average would be data total divided by 690 seconds.
Yes, I noticed there is a huge buffering phase in the beginning. I believe I can reset the bitrate measurements at any time, so I will start the measurement after the stream has been playing for a while and has reached "steady state". This way I should be able to completely avoid the buffer-filling start up effects, and also the resolution ramp-up in the beginning,