Recently faced the problem with custom content type folder.
When add publishing controls to you custom content type these fields are not saved and folder is not crated. Apperantly this behaviour is already spotted in SharePoint 2007 and was never fixed (for some good reasons I suppose).
So the solution we used was to inherite not from folder base type (0x120) but from document set content type with id “0x0120D520“.
In this way all publishing fields are possible to include in your custom content type;
Hope this helps,