I wasn't aware the validity of medical clearance had an impact on validity of green card? I thought once you got your green card ,you had 6 months to enter the US to use it. I wonder if this is also same with police clearances too then?
As for medical appointment in relation to your interview, I asked similar question here and was told at least a few weeks before interview. You will probably/definitely need to have 2 appointments for medical clearance as you need xrays and blood work. Additionally, you will require a seasonal flu shot if you get your clearance before 31st March as US flu season ends April 1st.