I think I understand your idea: you want to introduce some form of symmetry to this, by being able to classify a planet by its values on two axes as if it were a Dungeons & Dragons alignment. Symmetry is beautiful to many people. I understand this. I have sympathy for what you're attempting. However, I feel that your attempt to increase beauty by introducing symmetry is in fact decreasing beauty because it makes several horrible nonintuitive situations:
Your system requires that savannahs be hotter than deserts. I come from Johannesburg, which is in the savannah latitudes. The desert latitudes are north of us (that is, a hotter climate.) Yes, deserts are cold at night, but their average temperature is higher.
Your system requires us to separate Ice from Glacial planets and to accept that these are as different from one another as Tundra and Desert planets, or Ocean and Glacial planets.
Your system places Tundra closer to Savannah than to Continental, despite the issue that intuitively Savannah means "a planet halfway between Earth and Tattoine" and Tundra means "a planet halfway between Earth and Hoth." Surely they should be equidistant from Earth?
Your system makes Ocean dwellers uncomfortable on Continental planets like Earth despite Continental planets being mostly ocean. The vanilla system, where they are next to one another, avoids this issue.
Those are the intuitive, aesthetic issues I came up against. Separately to that, your system also has a gameplay issue which Oscot raised and which you seem to have dismissed out of hand. Let me see if I can restate it in such a way as to make it easier to understand. I'll number my steps so that if you disagree it's easier to point at exactly which step you disagree with.
1. The game concept of a Gaia world is that it be equally welcoming to everyone who goes there. This makes them desirable and worth fighting over, sparking conflict and creating interesting multiethnic populations.
2. Under your system such a planet is indeed "one step away" from their home planet type for the natives of Desert, Continental, Ocean and Ice planets: it differs only by one point on only one axis. This makes a Gaian planet as desirable as those species' second choice for planets. All is well so far.
3. However, such a planet is "two steps away" for dwellers of Wetland, Savannah, Tundra and Glacial planets: it differs by one point each on both axes. This makes a Gaian world as desirable as those species' third choice for planets. Since this makes them less desirable than almost half the planets in the galaxy, there's no particular reason why such species would feel strongly about such places.
4. As a result, only half of species will particularly want Gaian planets. Their game purpose - to spark conflict by being something that everyone wants - is thus lessened.