Sounds like you're on the right track with your update. Good luck!
Our son is 12 but I remember being sorely sleep-deprived when he was younger. I may not have any answers but you are not alone! And, sad to say, bedtime is still a source of argument with my husband. I continue to think earlier to bed leads to a happier and more functional child; my husband believes in "why create a fight, he'll go to bed when he's tired".
My husband and I both rarely go to bed before midnight and I can't imagine going to bed at 8:30. At least I have some "me time", or even some "us time", after our son goes to bed. (Maybe if you stay up till when you want to go to bed, you'd be so exhausted you wouldn't hear your daughter at 4:30AM. It may be lame but it's a thought!)
Some babies/kids need more or less sleep than the norm. Mine dropped naps by two, and usually maxed out at 11 hours for a night. I always envied the parents who had kids who slept 12-14 hours each day! And if we got him to bed later, he still woke up at the same time, but was crankier than all get out!
Truth be told, we had a hard time letting our child cry it out. In general, I believe in that method. I think it helps the child to self-soothe. But some kids are also more high-spirited and not as good at that. Mine tends towards ADD which is another whole discussion not to be started here. Self-soothing is not his strength but we work on it.
One thing I know...your child will not remember this crying in later years. (My earliest memories are around 3, my husband's and son's earliest memories are around 2.)
If your child is fed and dry, that is the majority of the battle. How do you know she is not hungry at that early hour? Is your child going through a growth spurt? Growth spurts require more fuel (food and sleep). Maybe it's time to step up the food intake during the day to hold her over through the night. Who knows?
My husband and I used to share the night and early morning wake-ups and/or feedings (I pumped religiously to have a supply for my husband). My husband wakes up better than me and needs less sleep. He used to get up in the middle of the night and stand by "Mr. Clock", our old-fashioned wind-up clock in the living room. The tick of the clock would soothe our son in the darkness and he would fall asleep again.
To this day, our son likes us to stay with him for a while when he's falling asleep. Some would warn against that practice, but that's when some of our best conversations happen.
Going in and soothing your daughter, saying go back to sleep, without picking her up may go a long way for you. If you're grumpy at that hour, it is hard. But it sounds like she really needs more sleep.
We always left soft stuffed animals in the crib to provide comfort and/or entertainment for our son. And, we would give him a bottle of water that he could access at any time. He would usually fall asleep again. If not, we'd hear him playing in the crib.
To this day, our son loves his stuffed animals. They are his comfort, his siblings (he's an only child), his confidants. We are his comfort and confidants as well, but you don't need to do it all. From experience, sometimes I think we didn't teach our son enough about self-soothing.
Back to your needs. Personally, I need my sleep or I'm a bear. If Mommy's not happy, no one's happy! But finding time for you and your husband is critical. Are there other things going on between all of you other than just the sleep issue? Is one of you jealous of the time spent with the baby? Are you mourning the loss of your free time and your expectations of what parenthood would be like? Been there, done that!
Do what you believe in your soul to be the answer. You can drive yourself nuts looking for answers everywhere. To be sure, consulting with books and others can be helpful. But what does your gut say is the answer that works for you after all of the input? Remember to look within for some answers, too. Maybe even sit down and write those thoughts down, taking the time to do this, if that's your style. The time will be well-spent, I suspect.
Like I said, I may not have answers but I feel for you! I hope you find the balance to be there for your daughter while doing what works for you and your husband, too.
Good luck and hang in there!