The JAR licence you have is already deemed to be a EASA licence.
When you convert any ratings that are not current (i.e. Require a PC to renew them) will be transferred to the back of the new EASA licence.
So you may receive a licence with nothing on the front and the expired ratings on the back.
There is no need to spend money on flight training simply to convert the licence.
The requirements to get ratings current again are the same with the old and the new licence as they are both EASA licences.