How to replicate others' results quickly?
As JeffE points out, trying to reproduce existing results before embarking on new endeavors is not a waste of time. It can be particularly useful, especially in tracking down issues that you have within your own code—or, perhaps, in the existing literature. My most-cited paper, and much of the research work currently ongoing within my group, came about precisely because I could not replicate an existing paper. As it turned out, there were some significant methodological problems in the existing literature, and this led to a fair bit of digging around, plus a lot of careful analysis to demonstrate what had happened and why. As I've also said, the issues we uncovered there indirectly led to a different line of inquiry that has already led to half a dozen additional manuscripts.

If you are determined to speed up the process, however, you might try to consider simplified versions of the research cases presented that can validate what you're working on. For instance, can you find a "prototype" problem whose solution would be known with your method as well as the existing methods? Can you find one or two test cases which can test most of what you're looking for? Can you devise a new problem that compares the two better than the existing cases, and is also simpler to execute?