I'm not familiar with reg other than the Australian ones.
Australian CAR (1988) 6.14 (4) states in part:
Subject to subregulation (5) and regulation 6.15, a medical certificate remains in force for the period set out on the certificate, being a period of not more than ......
Subregulation (5), referred to above, states:
A medical certificate expires:
(a) at the end of the period set out on the certificate; or,
(b) if CASA extends the period during which the certificate remains in force under regulation 6.15 - at the end of that extended period; or,
(c) if a new certificate is issued to a person who holds a current medical certificate and the appropriate day (essentially the day of issue by medico ... my note) for the new certifficate occurs before the current certificate is due to expire under paragraph (a) or (b) - on the appropriate day of the new certificate.
CAR 6.15 outlines the conditions one can use to apply for the extension of valitidity of a medical certificate.
No where is there a 30 day, or any grace, on a medical certificate.