You could theoretically place the single images in your Unity project as Sprites and attach them to the Spine Skeleton, as shown in the example scenes Spine Examples/Other Examples/Mix and Match and Spine Examples/Other Examples/Mix and Match Equip that come with the spine-unity unitypackage. You could then pack the atlas at runtime as in the examples, which would be only a small atlas per character.
However I would not recommend going down this path, as all your assets of the 420 folders should fit into two 2048x2048 textures. Having all characters on two atlas pages would be preferable in terms of draw calls, unless you always only have a single skin of the 432 showing in the whole scene.
Could you please post a screenshot of the Texture Pack Settings that you have used? Especially the Packing type under Output would effect the time and resources it takes to pack, did you try different settings here: Grid, Rectangles and Polygons? I would guess that e.g. Polygons could be problematic at such a high image count.
You could also try packing multiple smaller atlas pages by setting the Max width and Max height to e.g. 1024 or 512 instead of 2048.
Packing Skeleton and atlas separately
In general I would suggest not packing the texture atlas along with the skeleton, but exporting the Skeleton without the Atlas first (Texture atlas: Pack disabled), and then exporting the atlas separately as described here.
If this still fails, you could also try adding a very simple pack.json file in folders that you want separate pages for, and export the top directory with option Combine subdirectories enabled - it will then go over all your subdirectories and process them at once, with the pack.json files acting as atlas page separators.
