OK here are the secret weapons: a 30 degree "engraving" bit (need at least 1/2" of cutting length), a 150 degree v-bit (or tablesaw, which is what I used), and your profile bit of choice.
The key to making this work is taking advantage of what may be considered a liability - the "draft" angle produced by the 30 degree cutter. Let's say the drawer side is 1/2" thickness. So 0.5" * sin(15 deg) = 0.129" appoximately. This is the offset from the top to the bottom of the cut as produced by the bit. I'm sure this would work with any angle bit that produces 45 degrees or less of draft, but haven't provevn it yet.
The reason I point this out is that instead of pocketing the waste material (flat area clearing in VCarve Pro), it's faster to do a profile cut, before the v-carving. The drop-offs are so small they won't bind your machine.
Here's what thedrawings of the tails and pins look like: