3D plot: smooth plot on x axis

I have a 3D polygon plot and want to smooth the plot on the y axis (i.e. I want it to look like 'slices of a surface plot').

Consider this MWE (taken from here):

from mpl_toolkits.mplot3d import Axes3D
from matplotlib.collections import PolyCollection
import matplotlib.pyplot as plt
from matplotlib import colors as mcolors
import numpy as np
from scipy.stats import norm

fig = plt.figure()
ax = fig.gca(projection='3d')

xs = np.arange(-10, 10, 2)
verts = []
zs = [0.0, 1.0, 2.0, 3.0]

for z in zs:
    ys = np.random.rand(len(xs))
    ys[0], ys[-1] = 0, 0
    verts.append(list(zip(xs, ys)))

poly = PolyCollection(verts, facecolors=[mcolors.to_rgba('r', alpha=0.6),
                                         mcolors.to_rgba('g', alpha=0.6), 
                                         mcolors.to_rgba('b', alpha=0.6), 
                                         mcolors.to_rgba('y', alpha=0.6)])
poly.set_alpha(0.7)
ax.add_collection3d(poly, zs=zs, zdir='y')
ax.set_xlabel('X')
ax.set_xlim3d(-10, 10)
ax.set_ylabel('Y')
ax.set_ylim3d(-1, 4)
ax.set_zlabel('Z')
ax.set_zlim3d(0, 1)
plt.show()

Now, I want to replace the four plots with normal distributions (to ideally form continuous lines).

I have created the distributions here:

def get_xs(lwr_bound = -4, upr_bound = 4, n = 80):
    """ generates the x space betwee lwr_bound and upr_bound so that it has n intermediary steps """
    xs = np.arange(lwr_bound, upr_bound, (upr_bound - lwr_bound) / n) # x space -- number of points on l/r dimension
    return(xs)

xs = get_xs()

dists = [1, 2, 3, 4]

def get_distribution_params(list_):
    """ generates the distribution parameters (mu and sigma) for len(list_) distributions"""
    mus = []
    sigmas = []
    for i in range(len(dists)):
        mus.append(round((i + 1) + 0.1 * np.random.randint(0,10), 3))
        sigmas.append(round((i + 1) * .01 * np.random.randint(0,10), 3))
    return mus, sigmas

mus, sigmas = get_distribution_params(dists)

def get_distributions(list_, xs, mus, sigmas):
    """ generates len(list_) normal distributions, with different mu and sigma values """
    distributions = [] # distributions

    for i in range(len(list_)):
        x_ = xs
        z_ = norm.pdf(xs, loc = mus[i], scale = sigmas[0])
        distributions.append(list(zip(x_, z_)))
        #print(x_[60], z_[60])

    return distributions

distributions = get_distributions(list_ = dists, xs = xs, mus = mus, sigmas = sigmas)

But adding them to the code (with poly = PolyCollection(distributions, ...) and ax.add_collection3d(poly, zs=distributions, zdir='z') throws a ValueError (ValueError: input operand has more dimensions than allowed by the axis remapping) I cannot resolve.

from 3D plot: smooth plot on x axis