Dealing with unassigned clusters in (MiniBatch)KMeans? [duplicate]

I'm clustering a largeish dataset (3-4 million rows, 3+ features, all numeric), and I'm clustering with a large k (f~=2000). I'm not actually interested in finding clusters, I and just using kmeans because it relatively evenly partitions non-clustered data (by count). I need all clusters to be assigned to at least some data (ideally enough to do a linear regression on that cluster, so >50), but quite often the clustering fails and some clusters do not get assigned:

>>> mbkmeans = MiniBatchKMeans(n_clusters=2187)
>>> len(np.unique(mbkmeans.fit_predict(X)))
# .../k_means_.py:1381: RuntimeWarning: init_size=300 should be larger than k=2187. Setting it to 3*k
init_size=init_size)
2165
>>> kmeans.n_iter_
12


This is not due to duplicated data - in each dataset there are no more than 5% duplicated rows. I suspect it is due to the problem described at http://user.ceng.metu.edu.tr/~tcan/ceng465_f1314/Schedule/KMeansEmpty.html, whereby cluster centres end up in a no-man's land between two or more other clusters that are closer to all the intermediate data.

So, the question is, is there any general procedure for avoiding this problem?

And in particular, is there a way to do that in scikit-learn? Or is there a better set of arguments than the default for MiniBatchKmeans that I could use (there are a couple that I don't fully understand)?