I found a way to do it for anyone who stumbles on this anyways.
We need to replace the following line from the OP:
plt.axhline(y=0.002, xmin=0, xmax=1, hold=None)
We replace it with:
ax1.axhline(y=0.002,xmin=0,xmax=3,c="blue",linewidth=0.5,zorder=0)
ax2.axhline(y=0.002,xmin=0,xmax=3,c="blue",linewidth=0.5,zorder=0)
ax3.axhline(y=0.002,xmin=0,xmax=3,c="blue",linewidth=0.5,zorder=0)
This produces: