Unless you're a computer chip design engineer, I wouldn't recommend redesigning your CPU.. you may end up with nothing.
What I do see is way too much thermal paste (so much that it oozed everywhere). Clean off all the paste on the CPU, board, and heatsink with rubbing alcohol, then reapply a very thin coat only on the CPU. You can Google thermal paste application techniques, but I personally spread a thin coat with my finger on the entire CPU surface.. basically the exact area that the heatsink will touch because that's all that matters. Make sure you blow out dust from everything while you're in there using a can of compressed air.
Too much thermal paste is worse than too little.