Ok, let's see what we can do.
From your EASY, you are bfing between 530-630am, then 150 pm, then between 6-7pm, df at 1030, and that pesky nw between 2-3am.
I am wondering if she is reverse cycling her feeding. This occurs when a baby nurses more at night than during the day, and can happen for various reasons (including babies who have their days and nights mixed up, refluxers, etc.)
From
http://www.kellymom.com/bf/normal/reverse-cycling.html:
If mom is very distracted or busy during the day, baby may nurse more at night to make up for missed or shortened nursing sessions, or simply to get more uninterrupted time with mom. Also, if mom is away from baby during the day, baby may take just enough milk (by bottle or cup) to "take the edge off" his hunger, then wait for mom to return to get the bulk of his calories. Baby will typically nurse more often and/or longer than usual once mom returns. Reverse cycling is common for breastfed babies who are away from mom part of the day, especially those just starting out with the bottle.
The reason I'm thinking this is that most babies of this age go for one long stretch without a bf: through the night. However, because of your work schedule, your dd's long stretch is between 6am and 2pm - that's roughly 8 hours without a bf! So she's making up for it by feeding more frequently through the night - 2pm, 6-7pm, 10pm, 2am, 530-630am - on a pretty typical 4h routine. Does that make sense? Do you think that might be what's happening?
If that is what's happening, all you can do is try to up her milk intake during the day. When you offer milk in a sippy, what are you offering? Breastmilk/formula/dairy? I wonder if it's the sippy she's rejecting, or what's in it... (for example, if it's formula, it's much less sweet than breastmilk and has a very different flavour). You may have better luck offering expressed breastmilk. Have you tried offering the bottle rather than the sippy? Though some babies are quite proficient with the sippy cup by this age, they seem to be the exception rather than the rule. She may be more willing to take a milk feed from the bottle, though that will take some effort on your part too. I did it though with my ds in preparation for my return to work a few months ago, so it is possible!
Let me know what you think?