She sounds tough! I'm sure you are both very tired! I had an all night nurser though she didn't go anywhere near 16 times a night! DD was also a baby who was difficult to put down to sleep. Many people do decide to night wean around this age. I didn't. I actually found that my DD started nursing more around 18-19 mos for a few weeks, right before she started talking a lot. There is a reason they nurse so much, she needed to tank up for that development. That said, seems like your baby could do with some help to stop waking so much.
You said you read the No Cry Sleep Solution books, did you commit to implementing her ideas? You really have to be consistent for up to 3 weeks I think. Have you checked out Dr Jay Gordon's night weaning ideas? That may be helpful. http://www.drjaygordon.com/development/ap/sleep.asp
Sounds like your DD is overtired. When is she napping? I know people have said make sure she stops by 6 but wow, that seems so late to me. I'd make sure she isn't sleeping any later than 3:30 or 4. What time are you starting the night routine? Move it up so lights out is around 7/7:30 (I know this can be challenging if your DH is working, but you may just need to adjust). Once they get overtired the adrenaline kicks in and it's party time.
Is she getting outside time? That was really helpful for DD. What about screen time? If you do TV, you may want to cut that out, or if at all only do it first thing in the morning or something.
Have you considered food intolerances? Many babies and children who have sleep issues have them because of intolerances. Gluten, dairy, the other big allergens, and colors and chemicals in prepared foods can be an issue for some even if they aren't allergic to them. It can really contribute to behavior and sleep issues.
Do you cosleep? Do you use some sort of white noise? Have you tried some sort of music as a cue that it is going to bed time? How is your routine all day? If the daytime flow is pretty consistent that can be helpful.
Have you tried tanking her up with a bunch of nursings in the late afternoon/early evening before bedtime? What is she eating for supper? Make sure it's some protein and complex carb, rather than a bunch of white pasta or something that will cause a big sugar dip.
When she does wake up, try to keep your cool. If you are anxious (as I am sure you are) she will pick up on that and it will exacerbate the problem. If she wants to play, try to be as calm as possible and just not engage, don't talk, keep laying her back down and be as boring as possible. Offer water instead of nursing (not for all the nursing maybe, do it gradually).
Try not to talk to your friends who have good sleepers or your mother or whoever about it, it will just make you more anxious.Pedis are little help too. They are good for medical advice but generally know nothing about parenting stuff other than what they or their wife did. As another poster suggested, check out what Dr. Sears has to say about sleep, see if you have a local API or LLL group around so you can talk with other moms who nurse and don't CIO. And try to remember that you'll get there. I'm on the other side of it now, DD is 3. I remember feeling like I'd never sleep. You'll get there! Good luck.