Output queue length == number of packets waiting in line to be sent.
So, when you've maxed out your link, and still have "stuff" to send, it goes into the output queue, since it can't be immediately sent (on account of the link being at bandwidth capacity). Also why your ping response time gets high - those network packets have to wait in line too.
To fix this, you can get a fatter pipe, send less stuff, or (probably the best option) throttle your send rate as to avoid sending faster than your link can handle.
You can also try updating firmware and network drivers (as in the linked article), but as you've already stated that your WAN is saturated, that's not going to help. You're trying to send too much, too fast, so you end up with a queue. Better than having the traffic dropped.