S.I.
My honest opinion is, you can always throw away a paci, but you can't take away the thumb. My daughter was the same way, so I stayed with the pacifier. She would go around the house and play and when she really got busy she would leave her binky laying around. When I was ready to take it away, I would pick them up and put them in a drawer. Eventually, she was down to one, so I told her then that if she lost that one it was gone. Eventually, that one was lost too. I found it laying around and I kept it too. She fussed about it, but she was two, so I could talk to her and she understood. She went straight to sleep and hasn't asked for it since.