when should one seriously consider bankruptcy?
There's no litmus test. Generally it's indicated if you have high unsecured debt (medical bills, credit cards, utility bills) and assets to protect (like a car, savings account, or wages that could be garnished). There is also an income test to declare complete (Chapter 7) bankruptcy.
Bankruptcy can't get rid of student loans and you may still lose your house or your car. It affects your credit for 7 to 10 years. Also, you can't declare bankruptcy again for 6 years.
A bankruptcy lawyer would be more likely to advise bankruptcy if your money problems come from one-time bad luck like a divorce or medical problems, and not from years of poor spending habits.
I can't recommend a specific one but you could try creditcards.com or bankrate.com. You might also look into products offered by credit unions which are nonprofit community financial institutions.
I haven't paid interest in years via the 0% offers. Is this a bad idea for any reason?
Congrats. The only problem I can think of is if you apply for a bunch of new cards in a short period of time it could lower your credit score. Check out your report at annualcreditreport.com
I have heard that you can negotiate lowering finance rates with credit card companies. How low can you realistically get them to go? If you negotiate it once, can you try again later?
The best would be if you have a competing 0% offer in hand and you can threaten to switch your balance over. There are lots of forums and online resources for negotiating with credit card companies. I don't see why they wouldn't renegotiate as long as you have been sticking to the terms of the original deal.
Yes, I think that paying off your card with a tax refund is a great idea! It's like instantly earning 15%.