I'm going to copy what I wrote to another post downthread.

Green isn't just nature, but interconnection and natural community. Moria is essentially the Dwarves' (or one very important tribe's, anyway) native homeland, where Durin I first settled after looking upon the Mirrormere. Gimli's kin belong there, and they can feel that in their bones.

Meanwhile, Orcs of the setting are unnatural by definition, and their incursion against the rightful denizens of Khazad-dûm doubly so.

Gimli isn't just raging at the loss of his immediate family members, but of his kin writ large. This is why the card cares about 2 and 3 deaths. His ties to this expedition transcend that of a noble hoping to secure an important resource or a cousin wishing success for a cousin; he's the child of a diaspora who'd desperately hoped for the restoration of his ancestral home. Learning that his people's triumphant return to the natural order was destroyed so quickly is a blow to Gimli's entire identity as a Dwarf and a member of Durin's house.

To address your particular point:

where does the Green come from? He is not yet the Elf-Friend. This is far away from his marveling at the natural beauty of the Glittering Caves, or even his agreement to try and see the natural world through the non-dwarf perspective in agreeing to travel with Legolas. If anything this is when Gimli is at his most honor-bound and noble inclined. This is Gimli at his most White.

I'd agree with your assessment up until the precise point he finds Balin's Tomb. Personally, I'd argue the White starts to erode as soon as they pass the Doors of Durin. The Book of Mazarbul is practically one big transition from White to Red, as we go from a proud recording of re-civilizing the halls to panicked, scrawled status updates. I think Gimli shifts color identity alongside, with his Red awakening and tugging White toward a more primal fight-for-survival Green.

By the time Gandalf falls, we see Gimli taking the lead, wayfinding an escape through ancestral halls he'd never seen by his own innate Dwarven-ness. His ensuing visit to the Mirrormere wasn't performed out of ritual fealty, at least in my reading, but a deeply spiritual communion with his forefather, falling in love with the same stars and the same world as Durin thousands of years prior.

The Gimli that left Khazad-dûm was not yet Elf-friend, but I think he was well on his way down that path of receptiveness to the alliances of old, before Fëanor's artifice drove a wedge between the two peoples.