Um. This "bridged amplifier configuration", where you have two amps driving opposite sides of a speaker with one of them inverted, is pretty standard. It doesn't SUM the outputs, it does a DIFFERENCE, and V - (-V) == 2*V
Here's the circuit from TI's LM380 Audio Amp datasheet:
It's also commonly used with digital circuits (eg for developing a higher voltage across an LCD display, or getting more amplitude out of a piezo buzzer (both like HV, low current.) It's the basis for many capacitive voltage multipliers, and it's responsible for the "enter programming mode on RESET" bug that plagued early Unos until they added a diode...
That said, if you're trying to invert a signal that oscillates around 0V, you need a bipolar supply. Or you "redefine" "0"...
This looks like a good write-up: