Just to be clear - I am not judging re car seat - God knows I live in a glass house 
was only mentioning it
I asked the doctors to just keep ds and give him back when "he is fixed" (at 4 days old!) - 4 days of knowing something was wrong and being "fobbed off" and I cracked.
Its so difficult when you're being told there is nothing wrong but you can feel something isn't right.
Get a second opinion.
What have you ordered? Is it the cocoon thing? I looked at that but ds was a jolly giant once he actually started gaining weight, so wouldn't have been worth the expense.
We used books under the legs of crib, and a small had towel folded slightly under the mattress of the crib.
Only created a slight incline but just enough to help. He was also sleeping in a different position, not flat on back - however at 4 months I am assuming your daughter makes her own mind as to how she sleeps :)
Does your daughter look for you when she falls asleep during the day?
During the day, DS slept in a Chicco chair which could be reclined almost flat, but we were able to keep a small incline (I really rate the chair, as have the people I have loaned it to over the last 2 years). He is a nosy little beast, so like to be able to see around. Again, this helped keep him calm and sounds similar to what you are doing with the car seat. Fisher Price do a toddler chair which can still be tipped back. the "little" chairs suitable from early on may not be suitable, as certain we stopped using it when her was trying to sit up for fear of him toppling it over. The fisher price one is far more sturdy and could get one on ebay as cover is machine washable.
I used to sit on the floor facing him (leaning on the chair as always so tired!) one hand on his leg and watched box sets on the telly (TV behind him). Enough to remind him I was there, and I didn't feel stressed trying to soothe him for what felt like hours at a time knowing he needed to nap.