Unemployed EU citizen - Private health insurance or travel insurance?

I've recently moved to Germany and I'm looking for a job here.
After my registration as a resident, I tried to apply for public health insurance only to find I'm not eligible for it (I'm an EU citizen and I had no health insurance in my home country).
The problem is that I'm also having trouble applying for a private health insurance, even though I can afford it... Most companies reject me because I'm unemployed.
It's been one month now, and I'm afraid I won't be able to avoid any back charges. Would getting a travel insurance instead be a good idea? And switch to public health insurance as soon as I find a job?
Would that count as a normal health insurance?

Very few or no travel health insurances fulfills the German statutory requirements.
As far as I know, as a resident you must join a German (public or private) health insurance. If the public one already told you (get it in writing!) that you are not eloigible, the private ones must take you. Sometimes you have to be firm - and in all cases, apply for membership in writing and insist on a written rejection if they really don't accept you.