I want to feed the results of a clustering into a logistic regression Basically, my problem is, I have a dataset where I know about 12% of the rows should be classified as something, and I have some reasonable predictors. The problem is, my predictors aren't too good, because when I run a K-means with two clusters, they classify 85% of the rows as target instead of 12%. But otherwise the centroids elaborated seem to have face validity.
My idea is that I could feed the cluster assignments and the predictors into a logistic regression, and then I could fine tune the acceptance threshold to 12% instead of 50%. Mathematically, it seems like it should work but it reeks of inelegance.

Clustering is determined by the "geometry" of your data, i.e. by the "distances" between your data points, where "distance" is meant to be understood very broadly here. Classification, in your case I guess binary classification, is determined by the labels $\{0, 1\}$ of your data points.
There doesn't have to be any relation between the labels and the clustering of your data. E.g., you could have something like this:

Here, the blue points are labeled with $0$ and the red ones with $1$. This shows a situation where you have two clusters above each other, but this has nothing to do with the labels.
Thus, I would not get distracted by the clustering via k-means and would concentrate on classification alone. If your labels cannot be separated linearly, think about other classification methods, e.g. kernel logistic regression or SVM.
Having said that, the geometry can sometimes contain some indication about the labeling. And, if one knows about that, one can use this, via semi-supervised learning, to improve the classification. But one needs some evidence, e.g. via domain knowledge, that this connection between geometry and labeling is indeed the case.
