The DAME's receptionist will usually give you a stamp or piece of paper for a temporary two month medical certificate until the proper one arrives.
I think the CASA clerical staff are over worked and all data processing has a back log, which is also leading to over work and mistakes.
The woman at Avmed CASA was lovely and very helpful, but the suggestion of a Business Processing overhaul above has merit.
They should give DAMEs access to the Avmed system over the internet so they can update the details on the spot for an instant medical, then automatically mail the certificate.