How about a happy medium between everything you've gotten so far:
1. Confer with the extra lawyers. If they give you positive feedback...you can get a court order for the DNA test, you won't be on the hook for 15 years of child support, etc.
then...
2. Talk to a guidance counselor or child psychologist about taking the next steps. Do you sit down with the kid before having the test, do you stay in the background and let the process work, etc.
then...
3. Follow the answers in Step 2 and give them to the people in Step 1. Put the Psychologist in the same room as the lawyers (if you can afford it...$600/hr) and come up with a complete gameplan. Give them a clear idea of what you want. Have them develop a plan to follow at each step of the way.
4. Find out if there is a statute of limitations on the type of fraud that your ex committed. If there is criminal or civil liability that can be acted on, keep this in your back pocket and use in only if:
a) the daughter already knows what kind of a**hole her mom is and you form an immediate and strong bond, or
b) the ex fights you every single step of the way and you have no alternative but to get ugly.
5. I agree that you need to be above all of the dirt that WILL be flung. If you have contact with your daughter, you need to be very clear that any backlash from your attempt to connect is simply the result of mistakes that BOTH you and your ex made when you were young and naive. If it gets ugly your daughter WILL BLAME YOU FOR UPSETTING THE APPLE CART, at least initially.
6. Keep in mind, you can always back off if it gets too intense, but get your name and contact info in front of her somehow. People are naturally curious. It may take some time, but once she knows of you, she's going to want to hear your side of it...especially if you're within 12 miles of one another.