CALET, the Calorimetric Electron Telescope, launched to the International Space Station in August 2015 and in continuous operation since, has gathered over seven years of data so far. CALET is able to measure cosmic-ray (CR) electrons, nuclei, and gamma rays and with its 27 radiation length deep Total Absorption Calorimeter (TASC), measures particle energy, allowing for the determination of spectra and secondary to primary ratios of the more abundant CR nuclei through $_{28}$Ni, while the main charge detector (CHD) can measure Ultra-Heavy (UH) CR nuclei through $_{40}$Zr. CALET UHCR analyses use a special high duty cycle UH trigger with an expanded geometry that does not require passage through the TASC. To effectively analyze UHCR trigger events, a number of screens and corrections have been developed for the analysis. From time- and position-dependent detector response corrections based on $_{14}$Si and $_{26}$Fe, to an angle-dependent geomagnetic cutoff rigidity selections and minimum deposited energy screens, a number of methods have been explored to optimize UH statistics to varying effect. In this work, we aim to show how these event selection screens and corrections have been developed, how the rigidity screens shown previously by Rauch et al compare to the newer TASC methodology shown in our other ICRC paper, and how TASC selections may be used to influence analysis on the full UH-trigger dataset.