My daughter still sucks her binki; she's 30 months. Yeah, it annoys me. Like your daughter, she doesn't take it to daycare or get it during the day, but I noticed that she will start sucking fingers and thumbs if she's denied it when she really wants one. Maybe I'm paranoid, but I'd rather that she suck on a pacifier than her fingers (because breaking the thumb sucking habit is much worse than giving up pacifiers). Besides, pacifiers can be sterilized and she won't suck on anything else when we're out--on the other hand, if she started a thumb sucking habit, I can totally see her doing it with dirty hands, at stores, at the park, etc. And that habit would be constant!
She also has rather long hair and there were a couple days when she started sucking on that too... Ok, time to rethink the strategy--let's get that binki back!
I just took her to the dentist. He said that she needs to give up the pacifier by age 3 1/2 to 4. (I almost fell out of my chair... I intend her to be done with it way before then!) But he said her bite is fine and she very communicative; so there isn't a speech issue. So, I'm not stressing over the pacifier. My target is age 3, thats when the binki fairy will come...
By the way, I was totally gong-ho to end it 6 months ago. My husband asked me not to pursue it. Seriously. He said that on one of his business trips, he sat next to a woman who has a 5 yr old. They were talking and she said something that left a lasting impression: "If I had to do his toddler years again, I would only do 1 thing differently... I would not have taken away the pacifier cold turkey. Because once he lost that, I lost all leverage (for cooperation, good behavior)... There wasn't anything he wanted more than his pacifier and when that was gone, I was deep in the middle of the terrible 2's and 3's with nothing but sugar and candy to get him to cooperate."
Last thought, since your husband is deployed a lot, no doubt he already feels a little guilt about how his absences will affect your daughter... You might want to ease up on dictating how this will be resolved. Let him have his 2 cents. Don't steam roll him on it. My husband travels a lot for work and we met in the middle: I respected his input... She still can have her pacifier, but only for bedtime and not during the day, not in the car nor in the evenings. And he has to support me in telling her to take out the pacifier to talk.
I'm sure I'll be the 1% minority in the responses. Everyone else will tell you to "pull the plug". Do what you think is right, but I do think that with his military deployments and your 24 hour work schedule, you have a more unique situation than other families. Perhaps your daughter needs this comfort mechanism a bit longer than other toddlers who don't have to deal with daddy being gone.