I have seen this with my wife's computer. Though I haven't seen the large-window phenomenon (haven't looked), what I do see is dozens of active connections opened to the same destination, which of course defeats both TCP's link sharing and standard QoS algorithms.
I work around the issue by bucketing any Akamai IP ranges I find into a very-low-priority queue, and let those TCP connections fight it out. Seems to have worked well.
For those interested, here are the Akamai IP ranges I use:
23.0.0.0/12
23.32.0.0/11
23.64.0.0/14
23.72.0.0/13
104.64.0.0/10
2001:428:4403::/48
2001:428:4404::/48
2001:428:4405::/48
2001:428:4406::/48
2600:1400::/24