scardario's tips are definitely worth following. However, they are unlikely to fix the issue you are having. As you identified the class hierarchy change between 3.6 and 3.7 makes it hard to fix the serialization error you got.
One way I could imagine to get this working is to fork our runtime and integrate the latest RuntimeMeshComponent from
https://github.com/Koderz/RuntimeMeshComponent
which is supposedly working now with 4.20+. Our last version of the SpineSkeletonRendererComponent that use both spine-cpp and RuntimeMeshComponent can be found in this commit:
[ue4] Fixed up spine-cpp for use in UE4.@1454f8a
You might be able to just copy and paste this component over the current implementation that uses ProceduralMeshComponent. Of course you also have to add the latest RuntimeMeshComponent plugin to your project.
We had to switch way from RuntimeMeshComponent because it was unstable and not as well maintained as we needed it to be (i.e. it took months for the update to 4.20). Not a snark towards the author of the plugin! He does it in his free time mostly as far as we can gather, and we don't have the resources to help maintaining it.
Due to this, we decided to go with the in-built ProceduralMeshComponent, as that is maintained by Epic and unlikely to break in future UE4 versions. Sorry for the pain this causes in the short term. Long term, it should give us more stability, and less of this serialization nightmare.