Before “going on the market” — preferably a year or two before — call your old law school. Sometimes the school will have a faculty member appointed to help people like you. Even if it doesn’t, the dean’s office will often be glad to get you in touch with someone who can give you some advice.
It doesn’t matter that you never stayed in touch with your old faculty members. You don’t need personal contacts for this (though those never hurt): Many law schools see helping alumni get into law teaching as being part of their duties, and as being in their own interests, and will help you even if no-one at the school remembers who you are.
What can the advice do? It can help you avoid going on the market too early. It can give you a more realistic sense of your chances, so you won’t be too dispirited. It can help you format your resume more effectively. It can help you know what stage your new project should be in before you give it as a job talk. And once you reconnect with the school, you can get more than just advice: For instance, the school might arrange practice job talks, so that your real job talks are more effective.
I’ve seen quite a few people who went on the market far too early, or presented their resumes the wrong way, or made other mistakes that they might have avoided if they had some guidance. So call up the people who are most likely to be able to guide you. At worst, you’ll just waste a little time — at best, you can get some valuable help.