J.,
My son used a binkie (and not just for sleeping) until he was 3. I can relate to the parent shame.
We did our best to make our decisions about what was best for him (rather than what other people are comfortable with) although I do have to admit that I was really worried about what would happen, which probably interfered with my clarity.
We started (and when I say "we" I really mean my husband :) a conversation about it about 6 weeks before his birthday and on his 3rd birthday we went to the mailbox and sent all his binkies to the binky fairy (who, for us, lives in brooklyn NY) when we returned home (fancy logistics) she had left him a train table. He asked for his binky a few times that day (with tears maybe once) and then again the next day a bit, by the third day he didn't seem to notice.
He was very brave, and probably pretty ready to give it up.
This all happened before my daughter was born, and she has not taken to a binky, so I don't know about the challenges of co-binky-weaning.
I wish you good luck. And hope that it is a smooth transition for you all.