Thanks for your responses.
He IS getting too much cow's milk. In an average 24 hour period, he'll drink 36 to 42 oz. of milk at six different points through the day/night (if it's 2 percent or whole milk, I'll add some water). He mostly asks for milk around transition times: at 4am, 6am, 8am (while transitioning from sleepy mode to awake), 1pm (going down to nap for 2 to 3 hours), 3pm (while transitioning out of sleepy mode and into play) and 7pm (beginning of bedtime routine). I've started cutting some of the servings in half, so on a good day, his intake will be around 32 oz. In addition to this, he'll often ask for milk when he's feeling stressed or upset about something. Often I will give it to him (2 to 3 oz.). Sometimes I will try soothing him in other ways (holding, snuggling) and then get him playing so that he forgets about the milk. I've started doing this more in recent days. Sometimes this works, but not always. If he's sick, or if I'm low on emotional energy and less consistent in my responsiveness, he can drink upwards of 72 oz. a day and barely eat any solids!
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If I don't time snacks and lunches just right, (if I'm busy or distracted) he'll ask for milk and I have to work very hard to get him to eat food once he's got milk on the brain. I've tried night weaning (no milk from 7pm to 5am), but he continued to wake at 3 and 4 crying for milk, despite weeks of saying no, offering water, soothing by holding or rocking, etc. So I finally decided to adjust my expectations and give him a bottle at 3:30 or 4 and I leave a cooler bag with a second bottle for 6am in his bed so he can help himself.
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He's always been somewhat higher needs. It's always been very difficult to get him to sleep longer than 6 to 7 hours at a time. He seems particularly sensitive to my emotional state and those of others; he seems to be a pretty sensitive and empathic little person. I have always tried to be very responsive to his emotional needs; we are well connected and he's not an insecure boy, by any means. I think he has just come to rely on the bottle as his primary means of self soothing. I know I've helped it along, too, in that there are times that it is far easier to let him sit on the couch and soothe himself instead of staying with him longer. In fact, now that I've started to offer to stay with him longer, he often rejects my offer and prefers the bottle. (This is the double edged sword of no longer breastfeeding; you don't have physically stay with them for them to be receiving some form of soothing. I loved breastfeeding, but with him, it was also utterly exhausting to me!).
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I've tried a couple types of sippys, but every time I put milk in anything that is not a bottle, he gets upset and refuses it. I'm reluctant to spend more money on other kinds because I'm not convinced this will be an effective route for him at this point (it might have worked if I'd tried it when he was younger).
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I think I need to begin teaching him that there are other effective and healthier ways to soothe. And I probably should change my self talk and start thinking about it as introducing gradual, developmentally appropriate limits so he'll learn and grow, instead of thinking of it as "taking away" his primary means of self soothing (which makes me feel uncomfortable and anxious, and is not what I'm doing anyway).  Any suggestions on how to do that? Do you think that is still consistent with child led weaning principles?