Chicken - Egg problem with Job search, Anmeldung, and Health Insurance

Hi, My partner is a German citizen and I'm a non-EU citizen and we are moving to Berlin in September. Neither of us has a job in Berlin and I was trying to look for a job from abroad but it seems that I won't have a job until we get to Berlin. We thought that we would come to Berlin as tourists (I have an automatic tourist visa) and that I would have 90 days to look for a job. The thing is - we're required to Anmeldung (or at least to book an appointment) within 14 days and from the moment we Anmeldunged we have to have german health insurance, but since neither of us is employed we can't get into the public health insurance. We were looking at other options on how to get insured but couldn't find a way that is faster than getting a job. As I see it we have 3 choices.

1. Book an Anmeldung appointment and and appointment in the foreigners  in the far future and hope that I would get a job by then. The problem is that once I got a job I might have to wait for my far appointments. I also need to hope that I won't get into troubles for postponing the Anmeldung.

2. Do the Anmeldung and get a private health insurance - that would cost us 850 euros a month (including a baby) and it will require us to go through medical examinations first.

3. Cancel our flight and keep searching for a job from abroad.

What do you think? Do we have more options? Thanks!