Transiting giant exoplanets around M-dwarf stars (GEMS) are rare, owing to the low-mass host stars. However, the all-sky coverage of TESS has enabled the detection of an increasingly large number of them to enable statistical surveys like the Searching for GEMS survey. As part of this endeavor, we describe the observations of six transiting giant planets, which include precise mass measurements for two GEMS (K2-419Ab, TOI-6034b) and statistical validation for four systems, which includes validation and mass upper limits for three of them (TOI-5218b, TOI-5616b, TOI-5634Ab), while the fourth one--TOI-5414b is classified as a "likely planet." Our observations include radial velocities from the Habitable-zone Planet Finder on the Hobby-Eberly Telescope, and MAROON-X on Gemini-North, along with photometry and high-contrast imaging from multiple ground-based facilities. In addition to TESS photometry, K2-419Ab was also observed and statistically validated as part of the K2 mission in Campaigns 5 and 18, which provide precise orbital and planetary constraints despite the faint host star and long orbital period of ~20.4d. With an equilibrium temperature of only 380K, K2-419Ab is one of the coolest known well-characterized transiting planets. TOI-6034 has a late F-type companion about 40" away, making it the first GEMS host star to have an earlier main-sequence binary companion. These confirmations add to the existing small sample of confirmed transiting GEMS.

Cone search capability for table J/AJ/168/235/stars (List of targets (Table added by CDS))