After thinking about it for a while, I came up with the following process:
First I drilled my first hole using my dremel and glued a magnet inside so that it was flush with the outside. Then, I placed another magnet on top as can be seen above.
I then took the piece that I was going to magnetize this to and drilled a hole in that one, checking every so often to see whether it fit the magnet yet. When it did, I put some glue in the hole, then stuck the exposed magnet into the hole while still attached to the first magnet. Then I simply slid the two pieces off of one another (DO NOT pull) and let the superglue take hold.
By keeping the two magnets attached while I was drilling the second hole I made sure that the final product would still have a nice, strong connection between the two parts.
I then proceeded similarly with the other alternate weapons load outs, this time starting from the figure and placing the magnet on top that would go in the other weapon options.
So, if you're ever having trouble getting your magnets to stick (or even keeping the polarities in the right place), try keeping the magnets connected throughout the process- you'll see a much greater success rate in making that connection really secure. And if you drill too deep on the first or the second hole, don't worry- superglue or greenstuff should provide enough extra material to make sure that your magnet is in the right place.