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Okay, we have something to go on right here, you've got 5 good sized chunks of mesquite and 5 more of hickory. Consider the ratio of chunk to lump for a moment. That's one friggin whole hell of a $%!^load of mesquite, topped with way too much hickory for any Egg cook. You are aiming for a completely unneccessary level of smoke on your meat.
You are right about the combustion problem, and it's a problem you want to have, you'd never want to ignite that much chunk in an Egg. You get 95% of your smoke flavor from the lump in an Egg, what you add in very small amounts of chunks and chips is nothing more than subtley steering flavors to suit your tastes. For me, 5 chunks of mesquite will shave down to 5 years worth of briskets while the 5 chunks of hickory would last me 2 of those briskets and 3 shoulders after mixing with some apple, cherry, and blueberry.
You should give some serious consideration to the possbility that you prefer more smoke than the norm. Not that there is anything wrong with that, you just might not find a BGE solution to this problem.