I am very tempted to send in my Readiness to Interview form already too - but I'm afraid that they may give me an interview date a week from now and not have everything organised yet. As anxious as I am yet get an interview date, I think it'd be best to get things collected before you send the form in. I'd hate to get a date and then have to tell the Consulate that I am in fact not yet ready - I think that'd annoy them.
Surprisingly enough, getting the police check and medical doesn't seem too tricky or take that long. Like Kath suggested, get the test to get immunity and also get the jabs you think your fiance will need so that when it's time to get the medical the only thing that needs to be arranged is the X-Ray and the blood test for HIV and syphillis. And dependent on how busy the Doctor is, you may still need to wait for a vacancy with him too.
I think with so many variables in play (such as the Doctors' availability, when X-ray and blood test results can get done, etc) it'd be best to wait and be certain - I think it'll all pay off in the end.
Hope you get Packet 3 soon - I was beside myself when I received it last week

But it did take me 5 days to fill out and send off the DS-230 Part 1

I kept procrastinating over it...