It would be really cool for modpack makers to be able to create custom meshes.

This is already possible, and is the way Ex Deorum creates the default meshes, although that's on me for not documenting it. Here is the way to add a custom mesh to Ex Deorum:

1. Choose your mesh item. It can be anything! Doesn't matter if it's an Emerald Mesh you added with KubeJS or an Iron Pickaxe.
2. Add the item to the #exdeorum:sieve_meshes tag. This will allow players to insert the mesh item into an empty sieve.
3. Add a mesh texture for the mesh item in a resource pack with the following format: assets/modid/textures/item/mesh/mesh_item_id.png
   Replace modid with the mod id of the item (ex. minecraft, kubejs)
   and mesh_item_id with the id of your item (ex. iron_mesh, emerald_mesh).
   If you don't do this step, your mesh will appear as a magenta and black checkerboard in the sieve.
4. Add in the desired recipes using a datapack and specify the mesh item as your chosen mesh.

If some of this doesn't make sense, you can check out where Ex Deorum does this for its own sieve meshes in this GitHub repository. Relevant screenshots, in case you get stuck: