Exactly why Blizzard implemented rated battleground on later expansions.
I do not think your suggestion of having 2 different BGs can be implemented without intervening with Warmane's policy of being Blizzlike since they would need to put in an NPC somewhere for this special battleground to happen. What would be easier is to just have a minimum gearscore for BGs, which retail blizzard actually has right now. When they are fresh 80 with this x7 XP rate, they are around 2k gearscore. That means they are barely geared for Black Temple at their best. When they queue up, they can't even fight players. They will literally die from Shadowmounre UH DK's DOTS. That's the reality.
What I think is the best is to have a minimum gearscore of AT LEAST 4k+ (they won't get one shotted. probably 2 3 shotted but still) for BGs. I really don't think 4k+ is anything close to hard to achieve. You go AH, buy some blue/purple gears, you will be good enough to run FOS/POS. Get some more purpies, you will be good for BGs. For people "uh, I don't want PvE, I just wanna do PvP", there is a good server called BLACKROCK that you might wanna head yourself to AND you might not have noticed because you just donated for them but, take a look at your trinket (trinkets, if you are a human). GUESS WHAT? THOSE ARE FROM PVE RAIDS! OH MY GOD DUDE MIND BLOWN.