I am understanding that the grinder must be far enough away from any other areas which may spawn mobs? Your standing spot at the grinder should be 128 blocks away from any other spot that can spawn mobs.That has probably been mentioned a few times in this thread already.
Another very good option is to go to the End and build an Enderman grinder.If you build it 128 blocks above the surface and AFK to one side of your spawner, no caves will be in range. You need two stacks of cobblestone to build your tower, two stacks of ladders so you can get back up there again and one bucket of water to get down after you build it and you have made your start.Everything else you need, you would have needed had you built it on the ground. Have you reduced the view distance below 10 in an effort to increase frame rates? Mob spawning is severely reduced with view distances below 10 (at least currently in 1.8).Edit: I'd love to build it in the sky,but I have no motivation to dig up another 2000 blocks and rewatch that video, doing this all over. You don't have to light up every single cave to get spawns, however it will increase the amount you can receive.Most players typically have the cave systems below their area already lit up through normal play, however I would imagine some use x-ray.