Bluetooth Adapter Not Recognized by JBL Audio System (and other issues)

Here's a fun one, fellas.

I bought one of those bluetooth adapters that fits into the CD changer slot on 2004-9 Prii. I've had no issues with these before—I've installed them in three other cars: Car Radio Audio Adapter Bluetooth Aux Cable Microphone Handsfree Music Interface Disc Box for Toyota Reiz/Camry/Corolla|Bluetooth Car Kit| - AliExpress

My car is a 2004 with the JBL system and Nav, which is different than all the other cars I've installed these into, but I figured it would work. There was a DICE Electronics aux adapter plugged into the CD changer slot from a previous owner—that has always worked flawlessly. I took it out and installed the new bluetooth kit.

Despite numerous car re-starts, the audio system never recognizes the new device. It is on, and I can connect to it via bluetooth, but the car doesn't notice it.

Doing a little troubleshooting, I plugged the old DICE adapter back in (which has a 12-pin female slot in its wiring harness), and while the car was on, plugged the bluetooth adapter into that. Voila! My music is blaring through the speakers! HOWEVER, all the steering wheel buttons don't work now. Volume controls on the radio itself work, but inputs don't show up on the LCD display like they should. I turn off the car, turn it back on again, and the car now refuses to recognize the entire DICE system. Unplug the bluetooth adapter from the DICE wiring harness, restart the car, and the DICE system can be selected again and all controls are back to normal.

With the bluetooth adapter plugged directly into the CD changer slot, I get the same weird activity when it comes to steering wheel buttons and volume controls. In addition, if I'm playing from the tape deck, I can't control the volume whatsoever.

Any ideas? Kind of bizzarre. First issues I've ever had installing these kits. Does it have to do with the premium audio system? If so, how would I get around that?

Thanks, all!