Unsupervised text clustering using a driving list
Your direction of using k-means on term-document matrix is correct. To go further, you can

Use Weighted k-means

You can also try artificially boosting the weight for certain columns/variables (corresponding to your pre-specified list of words). This will force the similarity calculation to be dominated by those words.

Use Constrained k-means

You can read up more about constrained k-means algorithm: you can force certain points to be in the same cluster. In other words, if there are two documents containing words from the pre-specified list, they are forced to be in same cluster.

Alternative: Classification

If you know that there are only two clusters to be formed, why stick to only unsupervised learning? Depending on the application and availability of labelled data, you may think of it as a binary classification task using nearest neighbor or similar algorithm.