When it isn't connected as an inverter it clamps the voltage at 675mV, I'm not really sure why.

What is "it"? Is it the LM386 power amplifier? The DC output of an LM386 is at half the supply voltage and an input signal modulates it.

I have had this working connected as an inverter without inverting the signal or at least would be led to believe so from multisim.

Multisim usually makes many mistakes. Did you give it a good model of an LM386 power amplifier or is it using the model of a completely different opamp?

I have no problem using the amp circuit you posted except that it produces the half-wave. This isn't a mtter of having the piezo wires connected backwards because for the time being I was simulating it in multisim using a plain AC source. I'm not going to go ahead and build a circuit if I don't have some idea that it's working and I don't own a real scope to check a breadboarded circuit.

The output of a simple circuit is half-wave. A different more complicated circuit is full-wave.

Is there a way to stop it from chopping off the negative portion of the wave?

Use a full-wave rectifier circuit instead of a simple half-wave one.
Most e-drum circuits use a simple half-wave rectifier circuit and the polarity of the piezo is connected so that it produces a positive output voltage when it is hit.
But your 555 needs a negative trigger pulse.

 

Seems to be on the output of the op-amp, but I think I've found a circuit that will solve this problem entirely, as well as another and I think will use the LM324's I have.