My bearing packer has a cover that keeps the remaining grease clean. http://www.amazon.com/KD-Tools-2775-Bearing-Packer/dp/B0002NYDYE
As far as grease in the center....I just coat the inside of the hub with grease (not packed full) so when condensation forms it doesn't oxidize on the inside of the hub. Flaked bits of rust will damage the bearings along with any other particles that may be left inside a cleaned hub. The light coating of grease will help keep those particles out of the bearings. Filling the hub full of grease is just a waste of grease.

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