Actually, a typical Brown Bass has the thicker body and would handle a set up Series I electronics. The worst case, you might have to route a backplate for the preamp card on the upper body half.
We try to make the bodies as thin as possible to combat the weight issue. For the Series I and II, the pots themselves are physically larger and taller, so they need a thicker body than the components in other electronics models.
Price is, well, pricey. Series I electronics are 4300. This includes the pickups, electronics, power supply, cables, and calibration. You'd need to have a hum x cavity routed, and we'll need to drill mounting and access holes in the main backplate for the preamp unless we need to route an additional cavity with a new backplate on the upper body half. Installation would range from about $150-500 depending on the exact circumstances of your bass.
If you want to discuss it in more detail, please email
help@alembic.com and we can excahnge some specific information that we can get you a firm price quote for the job and arrange for servicing.
Then you need to figure out what to do with your surplus pickups and Anniversary electronics.