How do you controle zorder across twinx in matplotlib?

I'm trying to control the zorder of different plots across twinx axes. How can I get the blue noisy plots to appear in the background and the orange smoothed plots to appear in the foreground in this plot?

from matplotlib import pyplot as plt
import numpy as np
from  scipy.signal import savgol_filter

random = np.random.RandomState(0)
x1 = np.linspace(-10,10,500)**3 + random.normal(0, 100, size=500)
x2 = np.linspace(-10,10,500)**2 + random.normal(0, 100, size=500)

fig,ax1 = plt.subplots()
ax1.plot(x1, zorder=0)
ax1.plot(savgol_filter(x1,99,2), zorder=1)
ax2 = ax1.twinx()
ax2.plot(x2, zorder=0)
ax2.plot(savgol_filter(x2,99,2), zorder=1)
plt.show()

Similar to this thread, though not ideal, this is an approach using twiny along with twinx.

# set up plots
fig, ax1 = plt.subplots()

ax2 = ax1.twinx()
ax3 = ax1.twiny()
ax4 = ax2.twiny()

# background
ax1.plot(x1)
ax2.plot(x2)

# smoothed
ax3.plot(savgol_filter(x1,99,2), c='orange')
ax4.plot(savgol_filter(x2,99,2), c='orange')

# turn off extra ticks and labels
ax3.tick_params(axis='x', which='both', bottom=False, top=False)
ax4.tick_params(axis='x', which='both', bottom=False, top=False)
ax3.set_xticklabels([])
ax4.set_xticklabels([])

# fix zorder
ax1.set_zorder(1)
ax2.set_zorder(2)
ax3.set_zorder(3)
ax4.set_zorder(4)

plt.show()

Output: