There are more monsters in the continuities of Godzilla 2000, Megaguirus and GMK other than the ones that were seen on screen. After all, in GMK, Taizo Tachibana did say that "there have been numerous sightings in various counties". So we know that Godzilla, Baragon, Mothra and King Ghidorah aren't the only monsters in the GMK continuity. As for G2K and vs Megaguirus, if a giant radioactive reptilian monster and a giant dragonfly-like monster can exist, then certainly more monsters are out there. Maybe Anguirus, Rodan, Varan and Mothra?
Godzilla 2000 is not a stand alone movie despite it not making any references to any previous movie. It is another sequel to Godzilla (1954).
Godzilla (1998) is not canon with GMK. It just so happens that a monster that resembles Godzilla appeared in the United States a few years before the events in GMK happened. The subtitles didn't mentioned the year or the city that this Godzilla-like monster attacked. So it's possible that this unseen monster attacked, lets say, Los Angeles in 1997 or Miami in 1998 or whatever.
The reason why Prime Minister Machiko Tsuge from Godzilla Against Mechagodzilla said that Mothra was destroyed in 1961 and that Gaira was killed by the maser cannons instead of being killed by the volcano along with Sanda was because she was either thinking about other monsters or was too old to remember anything correctly or she was misinformed by somebody and didn't bother to do the research herself.
The Kamoebas that died in Tokyo S.O.S was the same one that appeared and, supposedly, attack Japan in 1987. Also, the amoeba that turned the mata-mata turtle in a second Kamoebas died some time after the events of Space Amoeba because it turns out that it couldn't live in Earth's atmosphere for too long due to certain elements in both the air and sea. So the amoeba died, but the second Kamoebas stayed the same. So no, I don't think that Godzilla was controlled by the amoeba in Tokyo S.O.S nor do I think that it is still lurking somewhere in the world of the Kiryu Saga.
It's possible that Godzilla fought and killed at least one other monster in the Final Wars continuity before he got trapped in the ice.