This is a really interesting use case for 2.5D rigs with backface culling! There isn't currently a dedicated "flip normals" or "invert orientation" button in Spine for attachments, so you're right that there's no direct one-click solution for this.
That said, here are some things worth considering as potential workarounds:
Using linked meshes
Linked meshes share their mesh structure (vertices, edges, texture coordinates, and weights) with a source mesh. If you can set up your source mesh correctly, a linked mesh with a different image could potentially save you from having to redo complex vertex placement. See the Spine User Guide on Linked Meshes for more details.
Copy/paste vertex positions
Spine supports copying and pasting vertex positions between attachments, as long as the same number of vertices is selected and the selection order matches. This could help you transfer a complex mesh layout from one attachment to another:

Adjusting texture coordinates manually
In mesh edit mode, with Deformed unchecked, you can move vertices to adjust texture coordinates (UVs) independently of the vertex positions in the scene. You could potentially mirror/flip the UVs manually by selecting all vertices and using the Modify tool. It's not a one-click solution, but it may be faster than repositioning each vertex individually.
Using the transform constraint trick for 2.5D depth
For 2.5D rigs specifically, you might also find it useful to use a transform constraint with a translate mix set to -100 to make a bone move in the opposite direction, which is the technique used in the Mix and Match and Owl examples for creating depth effects.
None of these are a perfect substitute for a true "flip normals" button, and your feature request sounds like a genuinely useful addition for 2.5D workflows. Hopefully it's something that gets considered for a future release!