So, just do whatever I said in that other post, except for a few more steps:

As for modded dimentions, they're stored the same way as well, except with different dimention IDs. For example, the DivineRPG mod uses realms less than -37 and greater than 48.

Since it's modded, just ensure that the configuration in your server matches the one in your client's config folder, otherwise bad things (ie. mismatched blocks) will happen.

Typically, the folders outside of the world folder store extra data (not world data) but more of additional metadata for newer versions of Forge. But, seeing how clean your installation is (ie. no extra data for the nether), they may just be old residue from old updates.

To be safe, just copy missing files from your outside folders into the ones in world.