I'm not sure what you see as a problem. If they are like mine, any time you put in grease it operates like a bearing repacker, forcing the old grease out. Bearing buddies just hold the grease against the outer bearing.
After my boat and trailer was delivered from Florida to RI, I pumped in grease until it came out fresh. At first it was pretty dead and loose, but after a bunch of squirts it came out clean. The old grease comes out from around the edges. Clean up is easy with paper towels.
If that's the type you have there should be no need to remove and repack your bearings at the end of the season.
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