For instance...
Godzilla 2000 - Hardly anything to change here. Maybe make mention of the fact that Godzilla isn't the only monster that's ever existed and this one could fit in with just about any timeline.
Godzilla vs. Megaguirus - Same as Godzilla 2000, and just remove the idea of Godzilla only having attacked Japan just a few times and this also fits into almost any timeline.
GMK - This one's not a tricky as you might think. Just mention that Godzilla (and other monsters) have been around for a long time, but Godzilla is now possessed and therefore stronger and more malevolent than before. Mothra is a deity, so her death isn't permanent. And as for Godzilla's death and possession, just mention that Ghidorah sacrificed itself to "cleanse" Godzilla, and either keep the beating heart to signify that Godzilla will regenerate, or just cut it altogether.
In fact, maybe the Godzilla in GMK is actually the resurrected original Godzilla and NOT the Godzilla from G2K or Megauirus, who simply doesn't show up here!
Godzilla x Mechagodzilla - Another easy one. Almost nothing has to be changed except for the idea that Godzilla hasn't been around much. In fact, a creative idea might be to say that the (resurrected original) Godzilla in GMK was harvested for its bones and used to create Kiryu...therefore the Godzilla we see in this film is the one from G2k and Megaguirus.
Godzilla: Tokyo SOS - Nothing needs to be changed, really. In fact, the whole "Mothra is here to take back the bones" plot-line works even better since she's basically finishing the job that she and the other ancient god monsters started in GMK.
Godzilla: Final Wars - The film already takes place in the future, so just say that Godzilla showed up again after Tokyo SOS and the Gotengo buried him in the arctic. Everything else can take place as it does without any problems...
Wow...that was even easier than I thought it would be. I might even just start thinking of the Millenium films as a cohesive series!

Anything I missed that might make this more difficult than I originally thought?