That would be the Millennium era, and of those six films, four of them featured a G with extra large and pointed dorsal spines. The first two Millennium films, Godzilla 2000 and Godzilla vs.
Just two years later in Godzilla, Mothra, and King Ghidorah: Giant Monsters All-Out Attack (2001), the dorsal plates were ... and his body hums and his spines glow in preparation for an attack.