How to publish analysis work of an approach worse that state-of-the-art?
Perhaps it would result in a paper that is too long to publish, but you might consider, at least, putting the two results into the same paper and giving an analysis of each case. 

Show how and why it works for one range, but, in a later section, show why it fails to work for the other. 

The overall suggestion here is that the analysis of the result and the possible insight it might bring to the general case is more important than each result individually. That is the perspective of a mathematician, anyway. The insight of the analysis/proof is more important than the theorem itself.