The Calorimetric Electron Telescope (CALET), launched to the ISS in August 2015 and in continuous operation since, measures cosmic-ray (CR) electrons, nuclei, and gamma rays. CALET, 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. Previous CALET UHCR analyses used a special high duty cycle ($\sim$90$\%$) UH trigger that does not require passage through the TASC and used time- and position-dependent detector response corrections based on $_{14}$Si and $_{26}$Fe and an angle-dependent geomagnetic cutoff rigidity selection to show abundances of even nuclei in agreement with SuperTIGER and ACE-CRIS. The work shown here further improves upon those results by restricting UH events to those that pass through both the TASC and CHD. While this constraint does reduce the number of events to $\sim$1/6 of the original UH trigger analysis, the loss of statistics is compensated by improvements in event selection from an energy-binned charge determination and minimum deposited energy that substitutes for the previous minimum geomagnetic rigidity selection. The results shown here represent 7 years of observation for the abundances of elements from Z=10 to Z=40 relative to $_{26}$Fe and are compared to previous measurements from ACE-CRIS, SuperTIGER, and HEAO-3