The pickup coil isn't really a Hall effect sensor. It's combination of a magnet and a coil of wire. It generates power when metal passes over it. It's more similar to AC power than DC.

This is the only positioning sensor our motorcycle has for electronically referencing piston position. Making a more powerful ignition control box would greatly benefit from incorporating additional sensors. I imagine our current one has a lot of safety-slop built in because of this.

I had an idea about doing that a while back.  I didn't follow-up on it though since I don't have ignition problems.
I did find that the DC CDI like is used on scooters has basically the same inputs.  It inputs both sides of the pickup coil, + and - 12v, and outputs + and - for the coil.

Seems to me that the timing pickup for those is 36º BTDC. I am not sure where our pickup is in relation to tdc.  That could be a game changer if it's very far off from that.  You'll probably also need to change to the small coil that is used by those CDI boxes. It would be nice to have a $25 CDI instead of the expensive box that is currently used.

The only real problem I see would be pickup position.  If it's too far from where it is on the scooter, it'll have to be moved or the idea dropped.

I was thinking about it more along the lines of something much easier and cheaper to get if the TCI box ever decided to go belly-up on me.  Just about any place that repairs chinese scooters will have one of the boxes and a coil.  

Many of the 4-wheelers also use the same box and coil. You just have to make sure it's DC instead of AC powered.

I contacted one of the manufacturers of the adjustable timing units one time and was told that the start and high end timing are the same as the standard. The only difference is the advance curve in the middle can be adjusted. They specifically said it won't increase the top-end timing at all so no additional top-end speed.