A.M.
hi, we did the same thing with the binky(went down to nap/bedtime). now im not sure if you were interested in taking the binky away, but at 3, this worked great for us. right after her 3rd birthday, we started talking about the binky fairy, and how she comes and gets all the binkys from the big kids to give to the babies at the hospital but she leaves any extra special present. we sat down and wrote the binky fairy and letter telling her the special present we would like. the first night, she changed her mind, but we kept talking about the special present she asked for. the 2nd night she was ready. we ran out to the mailbox and put all her binkies inside. she went to sleep fine. the next morning, we ran out to the mailbox and there were all presents inside. you could even put balloons or decorations to make it seem special. she was so excited. only 3 times since then did she ask for a binky, and we simply told her the binky fairy came and took them all and we didnt have any. she said she wanted them back and wanted us to get more at the store, then went to sleep and never said it again.
it was a great experience and at 3, her teeth shouldnt be damaged and she has the understanding to explain things like the binky fairy. also, dentists will prefer items that you can take away vs allowing something like thumbsucking to start.
for the other things, my nephew is the same way. he plays with the little tag on the back inside of his pants. big comfort thing. they have tried talking about it with him (3 1/2 yrs old) and he says he understands, but he just cant help himself. your daughter probaly feels safe because no matter what, her nipples are always with her, kwim. dont reintroduce the binky as its better to get rid of that for the teeth, but instead, try introducing something else, like a stuffed animal, blankie, maybe she would like a taggie blanket since its gives something tactile. or maybe try to find something more suitable for her to use like this http://panachechic.wordpress.com/2008/06/08/onyx-donut-sh... or maybe some sort of jelly bracelet. something she can use for comfort, but not to stand out too much. i know its not solving the problem, but some kids need that comfort to deal. and some people do have oral fixations.
since she is starting school, it might be a great time to try to introduce some new special object and have it be school only like have her only put on the necklace as she is leaving for school and take it off when she gets home. and just explain to her she cant put anything in her mouth at school but if she really needs something she can use her special necklace.
the only other option would be to just tell her she isnt allowed to put anything in her mouth at school per the teachers instructions, and just hope for the best. being around the other kids, she may be so distracted, she wont do it. unless they tell you she is doing it, you wouldnt even know, so it might not be an issue for either of you. maybe she stops, maybe she doesnt but its not detrimental. well, good luck to you, cant wait to hear how she does:)