Sorry for the misunderstanding. The original post was inaccurate. I'll update the information.
The asmdef files actually required a major reorganizing of the Spine-Unity asset folders.
This has been done in spine-unity for Spine 3.7 beta and it currently works fine.
For now, 3.6 can't be used with asmdef files without putting all the editor special folders into its own folder and giving it its own asmdef marked "Editor".
You should be able to do this yourself. Just follow the organization described above, or download Spine-Unity for Spine 3.7 and see how things are organized. There are no new features to be added in 3.6 so you should be fine doing this in your own project. Updating your project's Spine-Unity via unitypackage will still work because Unity detects individual files' guids when updating, even if they're moved to different folders.
The other option is to remove all your asmdef files when you build. But that may be very inconvenient depending on your setup.