Projects started in 13 or later have the benefit of objects being automatically replaced in the project in ArchiCAD 15 and 16. Projects started in 12 and earlier require that you replace those objects yourself. So your method would probably be the best way for such a project. You could of course select all identical objects at once using Find & Select to make things go quicker, but it all depends on the complexity of the project.
Try removing the migration libraries in the Library Manager. Then pay attention to the Library loading report and note which objects are missing. Find the ones that can be replaced by a newer part and do so. For the remaining parts that have no current equivalent you can then either add those parts one by one and embed them into the project or create a special linked library on a per project basis. A catch-all method is to save the file as a .PLA (ArchiCAD Archive format) which will store the placed objects with the file but that has its own pros and cons. You may have duplicate objects if you do not do some weeding first. Also, watch out for missing macros. If an object from a previous version is calling one or more macros then you want to make sure all the macros are present either embedded or in a linked library.