If you rejoin the special engine out procedure then follow the profile. This means cleaning up once out of the first turn, above acceleration altitude with recall items complete. You continue to follow the procedure until above MSA or you are happy to accept ATC vectors under radar control or you can achieve visual seperation from the terrain. When you have a chance and its safe to do so advise ATC of your special engine out procedure as they won't be familiar with it and they differ operator to operator depending on who drew it up.
Hope that helps