All the pieces to my project came together and I am very happy with the results. Will install the wheel on the car in a few weeks once I am back from vacation.
As a recap, I bought a Miata/Protege wheel off of eBay for $62. I then sourced an airbag for $50 off of a Mazda forum. I didn't like the scratches on the aluminum Mazda plate/badge on the front of the airbag so I decided to retrofit a 3D Mazda flying M logo on the wheel. I bought the chrome emblem for $20 and then scoured a carbon fiber insert for $18 total. Total cost for the wheel and all parts - $160. Compare that to the $400 - $800 for a RX7 Nardi or Spirit R wheel.
First, I removed the logo and found this:
I then used a razor knife to cut out the plastic middle. Sliced my fingers a few times before I found the best way of doing this - gloves and a putty knife to protect the airbag. Here is the result:
A few of the nicks around where I cut out were due to my stupidity but they don't show at all under normal light so I am okay with it.
I then cut out a plastic disc the size of the hole and used this as a mount for my chrome emblem. I used silicone adhesive to affix the chrome emblem to the plastic disc and I used two-way tape to affix the plastic disc and emblem to the airbag. Note I also used silicone to affix the disc to the airbag cover so if the airbag deploys, the chrome emblem and airbag cover will deploy properly. Finally, I bought a rubber o-ring and used this as a "sealer" around the chrome emblem. The o-ring gives the emblem a nice finished look. My end result?
Again, the flash magnifies the scratches I caused with the razor knife and also the dust on the emblem. In person, it looks great and I really like it. Will take pics once the wheel is installed.