it's not really that surprising that the top-ranked by CRI ends up being a colder temperature than the top-ranked by CFI. CRI Ra focuses on just a few desaturated tones which means it tends to score 4500K+ LEDs better. getting a high CRI at 2700K is extremely difficult.
CFI on the other hand covers a very wide range of tones, making it more representative of the perceptual fidelity you'll see. more red and orange tones are covered, so it's easiest to hit high scores with neutral CTs.