Thin channel GaN HEMTs intended for mm-wave operation suffer from increased on-resistance (RON) dispersion, limiting their large-signal performance. This work establishes a composite AlGaN/cGaN back barrier (BB) as a plausible solution to reduce the trapping in the BB while improving the 2DEG confinement. Large-signal characterisation at 28GHz, using source-and load-pull, indicates a significant improvement in PSAT and PAE for devices with an AlGaN/cGaN BB, compared to those with a cGaN BB only, due to their lower current collapse.