All JAR licences automatically became EASA licences in 2012 when Part-FCL came into effect. The idea was that when you renew the licence the CAA would send you one with EASA written on it. You can still do this, but it will come back with an expired SEP rating on the back. You would then have to send it back to have the SEP reinstated once you have renewed the SEP rating.
Much easier to do the necessary to renew the SEP and then convert/renew your JAR licence at the same time. The EASA way is assessment flight at an ATO/DTO, training as required & then a proficiency check. Since your SEP is more than 3 years expired the ATO is supposed to cover the entire pre-solo syllabus (not the hours, just the exercises) during the training as required phase, although I think they are allowed some discretion.
You can't convert your Aus licence as, technically, you already have an EASA (A) licence. You don't need a medical to renew or revalidate a class rating, I'm not sure if the licence renewal complicates that.