At that age, go with whatever works. You need some rest too. We went through the same thing with my son (we have twins) and he had the refulx too. Here are some ideas, and some things that worked.
1. Mattress wedge - they make these padded wedges that will give a little incline that may help.
2. Padding - good idea I see mentioned and if you tuck in a thicker blanket, she won't pull it out or anything.
3. Car seat - for a temporary solution, use it when you need it. Maybe every other day.
We actually DID let our son sleep IN the car seat, in the crib, all strapped in. Perfectly safe, and sleep is sleep. Just don't get TOO attached to it. We also used a baby swing that helped put him to sleep.
4. Sleep on stomach - I thought EVERYONE put their babies on their stomaches now. Try that, but keep a baby monitor going, and listen to make sure she's ok. Gotta watch that reflux when they're on their stomach.
5. Shifts - My wife and I also took/take turns on the "night shift" so ONE of you can get a good night's sleep. Or if dad is working, he can take the weekend shift. YOU need help and a break, and getting interrupted sleep, a couple hours here and there is only going to leave you exhausted and cranky, and not at your best for your baby girl. I'm a SAHD and your man can do ANY of these things.
Good luck, and hang in there. It gets easier, as I'm sure you remember.
Peace,
Richard