Please note when you open an older project in 4.0, under the covers it converts the animation data in the project to 4.0. For example, the curves are changed from the old way to the 4.0 way. When you export JSON from 4.0 to an older JSON version, you will unfortunately lose all the Bezier curves in your animations. This is because the way 4.0 stores the curves is incompatible with how curves are described in the older JSON.
You're likely better off running the JsonRollback tool yourself to convert 3.8 JSON to 3.6 JSON, that way you don't lose your Bezier curves. I think the tool doesn't actually support 3.6 JSON, but you can use 3.7 and the resulting JSON will work for 3.6 too.