Even if they were stand alone, (though the Two MechaGodzilla films were sequels to each other) they were still largely uninspiring films that lacked the creativity and heart of their 80-90s predecessors. GMK notwithstanding.
The 80's and 90's films, while creative in their own special way, doesn't exactly make them all that better. And heart? There's some, but its not as abundant as you might think.
Now, Godzilla 2000 doesn't connect to the original Godzilla film because there are no references that ties it to the original. Godzilla in that movie has always been there, we don't know if he's the first of his kind, or another member of his species. So that is stand alone.
Godzilla from Final Wars, this Godzilla is actually the original Godzilla, seeing how this is the only Godzilla who attacked in 1954 and was the only Godzilla to be documented at that time. Which is a creative aspect I find actually interesting.
This same element is introduced in Godzilla X Megaguirus and GMK in that their Godzillas are directly the original Godzilla. The only difference is that one did not die by the oxygen destoryer, and the other was brought back the hatred of the spirits of the fallen WWII soldiers that Japan forgotten.
The Kiryu Saga has one of the most creative aspects in that we have the original Godzilla technically battling as a Mecha/Cyborg against basically a second member of its species. Tied with 3 Mothras in the sequel who's directly tied to the original MOTHRA, and the revealing that Godzilla is drawn to Kiryu and perhaps only wants to bring his species back out to sea, like how Kiryu simply wants to rest in peace. It draws a creative aspect in that direction that takes a step forward in story-telling than most of the Heisei films. Plus there was the interesting aspect that if mankind didn't return the bones of the original Godzilla, Mothra wouldn't protect mankind anymore/Or potentially stop Godzilla.
I always found that point rather nicely constructed, like yeah, Mothra isn't always going to protect us if we mess up REAL bad, and I mean real bad.
The type of bad that even makes the goddess of peace go: WTF Humans!
And violating the scarcity of life of a creature we played a hand in turning into a monster, only to grave rob it and bring it back as a new form of monster/abomination of life isn't actually something that can be backed as a good thing. Even with good intentions, there's no way you can make that ugly fact better.
There are other creative aspects, like Orga and its origin (Which is extremely detailed in the Godzilla 2000 manga and pretty unique), Megaguirus and Dimension Tide, The Three Sacred Monsters(Added with the memorable notion of a good guy King Ghidorah), and there's the Xillians (Whose really been given some interesting creative detail, if you ignore the matrix/anime kind of style given to them), the Mutant Soldiers, Ghidorah's revamp from Monster X to Kaiser Ghidorah, Mothra and Gigan's origin, and the tweaking of Godzilla's origin along with his added grudge in taking down the brought back Gotengo.
The series is just as creative as the Heisei films. Now in terms of heart, that generally rests with the viewer themselves as its rather subjective. For example, GXM had heart because how certain scenes were done and the layout of the monster battles were pretty much a call back to the more, light-hearted times of Godzilla back in the Showa days. I feel the Kiryu Saga had heart as well in how they developed Kiryu's/Original Godzilla's character and the ending it had gotten in finally attaining eternal peace.
And yes, even though Final Wars is greatly outlandish in many ways with a poor assigned Director, this was also somewhat of a call back to the earlier days of Godzilla and how wild things got. Again, not the best director to go with, and definitely wasn't the best G-film of its respective era series. But what was done in several parts of the entire movie, it had some heart. Besides any G-film that bothers to not only remember but bring back Minilla entirely-
Has heart lol.