There is most definitely a real problem at the center of all these issues, they are not explained through player habits or environmental conditions as the op tested and addressed.
However, battleground ques have been pausing for as long as I can remember. Its only since wod release that the frequency and duration of those pauses has increased.
This is no doubt a result of something higher up the event chain and not the direct cause or source of long que times. Acknowledging that you can't enter a bg you aren't qued for, it probably has to do with the shuffling of eligible players for eligible bgs, exasperated by the new conditionals added to incorporate more bgs and the random feature, and the resulting pause as your character is moved from one list to another.
So that may make no sense at all to you, but I didn't post to try to explain what I don't know, I thought I'd post to give everyone some bandaids that players have been using for a long time.
Some of you have tried relogging and reloading with some success, but for those of you who stare at your paused que for hours or happen to be farming herbs in china, start typing /reload.
The second method involves chilling out maxing relaxing outside your major city of choice. This is my preferred method of smacking blizzard servers on the side of the cooling case. All you have to do is phase into the city (walk through the gates of org or sw) and walk back out to achieve the same result as the first method.
The last method is the most effective and most passive. Que bg, speak to flight master, fly anywhere. This works really well because when on flight path you are constantly changing zones and on extended flights you can kick back while effectively reloading your bg que every few seconds. Of course there is money involved with flying right, but if you have the gold and would rather not spam relog or look like a lost child running in and out of cities, this is by far the most efficient way to get your bg to pop.