All right! I took the D'Addario XL nickel untapered .135 off my Fender and threw it on the BB76. First of all, it did NOT fit in the saddle. It hung on the sides of the groove, and I could see empty space underneath it! That's not good. But...
In piezo mode, there was NO difference in response compared to the other strings. In fact, the .135 sounded better than the .128 because it was closer to the other strings in tension than the Carvin B. Good to know!
Shows me for believing other bassists on the internet...
Good on you for not doing the same! 
However, the non tapered string made the action much higher. Because of this there was actually a big drop-off on the magnetic side of the pre. Might be looking into, although it looked like the string height on your bass was even enough in the pics.
Anyway, good luck! Hope I've offered some help and not just confusion!
In piezo mode, there was NO difference in response compared to the other strings. In fact, the .135 sounded better than the .128 because it was closer to the other strings in tension than the Carvin B. Good to know!
Shows me for believing other bassists on the internet...
However, the non tapered string made the action much higher. Because of this there was actually a big drop-off on the magnetic side of the pre. Might be looking into, although it looked like the string height on your bass was even enough in the pics.
Anyway, good luck! Hope I've offered some help and not just confusion!