Why does matplotlib.ticker.MaxNLocator(prune='both') not prune my tick labels?

Question

I am trying to make a plot including a number of subplots, and I want them to share their axes. I have been trying to use matplotlib.ticker.MaxNLocator to do prune the labels on my ticks, so the figure has readable axes. However, regardless of whether I use prune='upper', 'lower', or 'both', I end up with labels which overlap each other, as shown in the image below:

An ever so slightly simplified version of the code I am using (although still fairly long, sorry) is below:

import numpy as np
import matplotlib as mpl
import matplotlib.pyplot as plt
import matplotlib.ticker as tck

chains = np.array([[-.4, 4, 0, 0, 0], [6, 19, 2000, 2.1e16, 6.1e13]])
pars   = np.array([r'$SF_\infty$', r'$\tau_D$', r'$\tau$', 'width', 'scale'])
nplots = len(chains[0,:]) - 1

# Fix up matplotlib to give plots like you like
mpl.rcParams.update({'font.size': 6, 'font.family': 'serif', 'mathtext.fontset': 'cm', 'mathtext.rm': 'serif',
    'lines.linewidth': .7, 'xtick.top': True, 'ytick.right': True})

# Make a plot
fig = plt.figure()
for i in range(1,nplots+1):
    for j in range(nplots):
        if (j<i):
            ax = plt.subplot(nplots, nplots, (i-1)*nplots+j+1)
            plt.plot(chains[ :, j ], chains[ :, i ], '.-', markersize=0.3, alpha=0.5)

            # Set aspect
            xlim, ylim = ax.get_xlim(), ax.get_ylim()
            ax.axis([xlim[0], xlim[1], ylim[0], ylim[1]])
            ax.set_aspect( float(xlim[1]-xlim[0]) / (ylim[1]-ylim[0]) )

            # Print things around the edges
            if (j == 0):        plt.ylabel(pars[i])
            if (i == nplots):   plt.xlabel(pars[j])
            if (j != 0):        ax.tick_params(labelleft=False)
            if (i != nplots):   ax.tick_params(labelbottom=False)
            if (j != i-1):
                ax.get_xaxis().get_offset_text().set_visible(False)
                ax.get_yaxis().get_offset_text().set_visible(False)
            # End if-statements

            # Fix tickers
            ax.minorticks_on()
            ax.tick_params(which='both', direction='inout', width=0.5)
            ax.xaxis.set_major_locator(tck.MaxNLocator(nbins=5, prune='both'))
            ax.yaxis.set_major_locator(tck.MaxNLocator(nbins=5, prune='both'))

# Saving file
plt.subplots_adjust(hspace=0, wspace=-.58)
plt.savefig('testing.png', dpi=400, bbox_inches='tight')
plt.close('all')

What am I misunderstanding in my usage of the MaxNLocator function? I am using Matplotlib 2.0.0.

(Also obviously, any comments on how to improve this plot for readability and decrease the amount of hard-coding is much appreciated!)