I don't see any reason for you to turn your phone off. I think keeping track of how many minutes you use is the best way to go. I have Sprint and I have am able to check my minutes on the internet, by automated message, or even calling a live representative if need be. You need to find out what your plan is, and monitor your own phone habits. If somebody call you during your anytime/day minutes, ask them to call you wherever you are at the time, or ask if you could call them back when you can get to another phone. I am sure most of your calls aren't "emergencies." Rather than sending out a mass e-mail, or anything to that effect, as they call, simply say something like, "Hey, I'm sorry. I don't have unlimited minutes, so do you think I can call you from another phone in a while?" Perhaps that way you can be subtle, yet they still get the hint.
Best of luck! I've been where you've been, and it really sucks. I'm sorry.