Resolved Question: can anyone give me some health insurance companys' websites with which producers can get appointed?

Well, you can't just go to the website, and click "appoint me!" and be appointed. You need to MARKET YOURSELF. Hint here, if you can't market yourself well enough to get an appointment, you're probably not going to be able to sell enough to keep that ppointment.

Unless you have an existing book to roll over to a new carrier, your best bet is hooking up with an existing agent, and using their contracts for a commission split, to build your book.