If you don't need to rescale the plot, I would plot against the positive angles 0-360 and manually re-label the ticks:
fig, ax = plt.subplots()
(df.assign(Angle=df['MM Initial Angle']%360)
.plot(x='Angle', y=['QM Energy','MM Initial Energy'], ax=ax)
)
ax.xaxis.set_major_locator(MultipleLocator(20))
x_ticks = ax.get_xticks()
x_ticks = [t-360 if t>180 else t for t in x_ticks]
ax.set_xticklabels(x_ticks)
plt.plot()
Output:

