Well, after a little bit of fenangling, I managed to figure out a way to do this, so I thought I'd share in case anyone else ever needs to disassemble their vanity mirros.
When you pop off the clear lenses, you're greeted to the bulb, and a plastic "rivet" that secures the front frame to the in-visor frame. Note that in the picture below with the incandescent bulb still in place, I've already drilled the "rivet", there's just one on either side of the mirror above each bulb.
I drilled both rivets with a 15/32 drill bit, and then used a small flat-tip screwdriver to pry back each of the four tabs (two per side) starting with bottom tabs below each bulb. Be careful - the glass is sandwiched in between the front frame and the visor, and could slip out during this step. When you pop out all four tabs (circled in red below), you can get access to the sockets for both 74-size bulbs and pry them out - I used the same small flat-trip to get each one out.
Lastly, with the LEDs in, I picked up small machine-head Phllips to replace the rivets - you'll need to size appropriately depending on the size of hole you drilled.
And voila, I can now truly claim having finished a full LED interior conversoin.
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