This was a lightning talk I gave at the NANOGrav Fall 2020 meeting. Our project to test the Strong Equivalence Principle with PSR J0337+1715 did precision pulsar timing using the same telescopes in the same modes as NANOGrav but we found we needed to analyze the observations differently. So this is a lightning talk to point out some of the things we did differently and spark discussion about why. Most notably we found the polarization calibration procedure inadequate and so we implemented a procedure that fits for the polarization calibration simultaneously with fitting for the pulse arrival time; as a happy side-effect, polarization structure in the pulsar signal helps constrain pulse arrival times. You can read the slides, or the video is below (only the five minutes starting at 0:17 is my talk):