I feel your pain darlin'. My daughter was all over the place with sleep and eating.
First... don't assume he doesn't need the nutrition. Babies are operating on basic instinct. They aren't trying to manipulate. You CAN'T spoil your baby at this age. You CAN'T. Letting him 'cry it out' is only going to frustrate you and him. He NEEDS to know you are there to meet ALL his needs. The CIO method just teaches that you WON'T be there to meet his needs and he has to sort himself out on his own. He's too little to understand this concept.
Second... three months. GROWTH SPURT! He may be growing ALOT and therefore needs more milk. Try nursing more often late in the evening to 'tank him up'. Also, try to nurse not in bed. Sit in a chair and rock him.
Third, as already suggested try coating the binki with your milk.
Fourth, also don't assume you don't have the milk to supply his needs. The lactation process is a supply and demand process. However, around the 3 month mark you and baby are really getting 'in sync' ... so you won't necessarily 'feel full' all the time... even when you are. Your body is adjusting to what he takes and is not making any more. BUT if baby increases the demand your body WILL MAKE MORE. It is VERY rare that a woman doesn't have enough milk to feed her child. It is MORE common to have too much milk. The body is a wonderful system and it will adjust to meet your sons needs.
Now, that being said... if he isn't really sucking for FOOD... but for comfort.. .your body knows the difference in that as well. To see if he is sucking for food... notice his jaw muscle. Is it engaged all the way back to the ear? Also, is there a couple of short sucks followed by a long suck? (long suck like you're drinking through a straw ... suck on your finger as if it is a straw to see the chin action) If you see these things ... then baby is sucking for FOOD. If not, then it is for comfort. And no.. you don't want to be the pacifier. It will take some time...but by offering a binki that tastes like mamma... I think you can coax him into taking it.
Change the routine. It will alert baby to the change and ease him into something new.
Yes, you are the parent and he is the child ... but we are here to teach our children... not train them like dogs. We need to TEACH them to soothe themselves. TEACH them how to meet their needs. Not train them to fit our sterotype of a perfect baby. CIO doesn't teach. It offers NO resources for baby to soothe themselves. Rocking, walking, sushing, stroking, soothing music... these TEACH our babies how to soothe themselves. It gives them tools.
Be patient. Also keep in mind every baby is different. Some babies WILL sleep through the night. Others will not. No two babies are alike and all have different needs. My daughter is VERY active. She likes to interact with people and be where the action is. Friends of ours... their daughter who is just 3 days younger is content to just sit and watch everything. Try lots of different things but keep in mind baby will let you know what works for him.