Using Diffuse Magic, Glyph Guard and Zen Med you can eat a few of them. You can generally eat the first 3 casts without any cooldowns, having a disc priest bubble for the cast is very helpful too. Guard on the 4th, Diffuse the 5th, Fort Brew/Guard the 6th, Zen Med the 7th. There's really no reason to have stacks higher than 7 if you're doing the alternating strat.
I noticed a few times that you'd have to time ZM right for that 7th one. OR just have the OT pick up the shredder at first, take the 7th debuff during his cast, then pick up the shredder from the OT. Once you get the coordination down for swapping the boss around, it becomes second nature and you can do it in your sleep.