So here's the update:
Antigravity, the battery manufacturer, thinks there may be a problem with the battery I purchased. They are exchanging it for a heavy duty lithium battery. In the meantime, my dealer has ordered me a new turn signal module. When the new module arrives, I will bring the car to the dealership to have it installed and have them check the electrical connections for any parasitic draw on the battery, and any potential shorts.
The new battery that Antigravity is recommending is their ATX-20HD.
Hopefully the new battery works out for me.
How did the new AntiGravity battery work out? Did you get the ATX20HD?