What's the most efficient/effective method for removing the rind of a well-ripened Brie? My family really loves "cheese crack", i.e. the "savory toasted cheese" from Digby.. (Our proportions: 1 block cream cheese, 1 stick butter, 1 wedge of ripe Brie. Cut up, nuke, stir. Seriously, try it.) 

The only problem is that the rind of Brie doesn't melt, so leaving it on leads to oddly-textured bits floating around unpleasantly in your cheese dip. Thus, we need to cut off the rind of the Brie. If it's a mild and firm (read: less ripe and flavorful) Brie, this is easy enough, but when your Brie is at that perfect stage of almost-but-not-quite-oozing-out-of-the-package, like Wegman's store-brand "Intense" Brie, it gets... harder. And messier. And worst of all, more wasteful of all that yummy Brie flavor.

Is there a trick or technique for removing the rind, so that you don't leave behind little bits that'll ruin the texture of the end product, but you also don't end up leaving half the cheese on the cutting board?

Alternatively, the frame challenge: is there actually a way to get the rind to melt? I wouldn't object to a stovetop method - after all, we only use the microwave if we're making a single batch. I know some people use slow cookers to make large batches, but AFAIK that still involves removing the rind.
Addressing the frame challenge: I forgot about the Brie in the cheese drawer for a bit too long. It was nearly liquid, so there was no hope of removing the rind; I was happy just to get the plastic wrap off.

I put it on the stove with some butter and heated it on low for quite a while, stirring frequently. Eventually I added the cream cheese. (Twice the usual amount, because it wasn't "coming together" without it.) Then I put it through a fairly fine-mesh strainer. The result is slightly grainy (for lack of a better term), but not unpleasantly so. However, it was enough extra work that I think a less-ripe Brie, properly "peeled", is the better way to go.