Can I publish an improved variation of a prior method or/and the results I found using it?
Incremental improvement of research methods is a major part of the purpose of academic research, so yes, an improved variation of an existing method is absolutely a publishable result.  From your description of the research, it appears that you have undertaken a comparison of predictive accuracy for the original method and your variation, and this has good results.

Make sure your paper gives a good introduction and literature review, with a fair summary of existing methods and your points of departure for these methods. It is okay to put your method forward as being superior to the original method it is varying (assuming you can back this up with predictive results or other relevant evidence), but obviously you would write this in a way that is respectful towards the progenitor of the original method.  There is nothing offensive to a researcher in taking a method they have developed and varying it to improve its performance.  As long as you are not unduly critical of the original research, I see no reason that your research would set you in conflict with the original researcher of the method.  It is probably even worth listing the author of the original model as a suggested referee for your own paper.