My baby seems to only want mommy
Why do you have to "get up" for a middle of the night feeding? Stay up with your family until the baby is ready for bed, then tuck the bub into bed with you and dream feed through the night. That way, you get your sleep and the baby doesn't have to cry for you (although crying in the arms of his loving dad is vastly preferable to crying alone in a dark room!)
I think the system you have with your husband is great! We have a similar deal, only backwards. He gets up with her in the mornings after her 7am-ish feeding and then I go back to sleep until he goes to work. We are starting to have some of the same mommy-preference stuff here, but not as strong as she is still younger than your LO and a little less aware. I would just try to keep doing what you are doing, but I don't know how bad the crying with daddy gets. Have you been stepping in to comfort her? Or letting him take and keep the lead?
Most babies go through phases where they want their Mamas and no one else will do. It's completely normal and healthy. It's just part of Attachment.
I don't really see the problem. You are, usually, sleeping 7 solid hours. Does your baby go to sleep at 9:00 at the same time you do? If so, he's sleeping a solid 7 hours, (which is a lot more than any of my babies did at even twice that age.) If he wants his Mama, it's normal and healthy. Babies are supposed to prefer ONE caregiver and 9 times out of 10, it's Mama. I know my kids loved their Papa, but when they were upset, they overwhelmingly wanted me first for at least the first 2-4 years of life. Babies usually form a strong attachment with ONE person at a time, and most of the time, that's with the mother. That's how Nature intended it (she's the one with the milk and the right scent and the familiar warmth) and it's simply healthy to allow the baby to have your presence when he needs it.
My kids, when they were babies, could be facing an other direction and know the instant my foot crossed over the doorway and immediately start crying. My DH and I always took that as a good thing. Our kids knew their Mama, wanted her presence and they were given what they needed, which I could easily give, just by being there and using my arms and my breasts to comfort our baby. Neither my husband nor I ever saw this as an unusual thing, just a normal healthy part of the Attachment process.
As for Night Time Parenting, my husband would often rock babies to sleep, but he was the one off to bed at 9:00 PM because he has to be up for work at 4:30 AM every morning. Usually the baby would be in bed with us, if the baby was wakeful and noisy and trying to wake Papa up (older babies sometimes smacking him on the face and yelling, "PAPA!" I have videos of it, pretty funny!) I would take them into an other room until they were asleep or quieter. Then we'd all be back in bed together.
As long as Dad is around and involved, "the balance" will happen as it is meant to. Parenting never was, and never will be "50/50." (That's one of the reasons the name of the original magazine, and the website is "Mothering." ) Moms usually mother more, that's just kind of the way it is. You don't have to do anything to "tip" the "balance" at all. Be there when your son needs you and it will work out.
We never did anything to "balance" anything ever. I did Mom stuff and he did Papa stuff. Yes, of course he changed diapers and rocked babies, but he also worked 40-55 hours a week, I did part time child care and then part time Lactation Consulting and did the Mothering as I saw fit. Of course I spent more time with the kids than he did. We never felt any need to "even things up." Like I said, nothing is ever "50/50" it becomes artificial if you try to make it so. Just care for your son as he needs it and Nature will take care of any need for "balance."
Honestly, I've never given any "balance" any thought, and I've been mothering for 27 years. We just both did what seemed to work at the moment. It worked out.