The 13 Middos used to expound the Torah Part 2

The Gemara in Zevachim (50-51) has a long discussion about whether something learned out with one of the 13 middos can be used again with the 13 middos to learn something else out. For example can a halacha learned out from a gezera shava be used to learn a gezera shava to another halacha to learn a second halacha. For some middos the Gemara has a dispute for others the Gemara leaves it as a תיקו. Here is a nice chart from the Artscroll Gemara summarizing things:

The obvious question is how can this be? The 13 Middos were given to Moshe to use to expound the written torah. How can there be a fundamental dispute about how they are used? You can't answer אלו ואלו דברי אלוקים חיים because they are mutually exclusive. What happened to the mesora? How can there be a dispute about such a fundamental issue?

Here is a link to Part 1