Class 2 initials can be done by the AME, so it won't make much difference anyway.
From the relevant JARs (Class 2):
(b) If a licence holder allows his Medical Certificate to expire by more than five years, renewal
shall require an initial aeromedical examination. Prior to the certificate issue the relevant medical records
shall be obtained by the AME.
(c) If a licence holder allows his Medical Certificate to expire by more than two years but less than
five years, renewal shall require the prescribed examination to be performed. Prior to the examination the
relevant medical records shall be obtained by the AME.
(d) If a licence holder allows his certificate to expire by less than two years, renewal shall require
the prescribed examination to be performed.