I think she's overtired. 2.5hrs awake time is a lot for her age, you might have better luck if you bring her first nap earlier. If she wakes early from her nap, do you try to resettle her before getting her up? You say she is sleepy, so maybe she would go back to sleep? So as a guide, about 2hrs awake time (including feeding and wind down) is probably the max that she can handle, even after a long nap. After a short nap, you'll need to cut that back even more to just maybe 1.5hrs.
She's also old enough now that you can do PUPD with her if shush-pat doesn't seem to help. A lullaby CD is a great idea!