I'm doing something very similar.
I have a 137 visa going through and
expect the med and police requests in the next couple of weeks.
I also
have a sponsored 457 visa going through at the moment, and have obtained
two sets of police checks, but only one set of full medicals, (we only
need X-Rays for the adults under the 457, but full meds for the
children) but for logistic purposes did the whole lot in one go.
The
medicals will go to Sydney in with a covering letter requesting them to
be forwarded to Adelaide once the 457 is complete. My migration agent
didn't think that this would be a problem.