You need to stop using the car seat all the time. Otherwise you will just prolong the misery (yours and his). He will expect the car seat and, when he won't get it, he won't sleep well. Then, when he does get it, he'll start expecting it again and it becomes a vicious cycle.
Before you do start the sleep training, though, I suggest you try to get some extra sleep. When you're tired, it's very easy to decide to go back to the old ways which sort of helped for the short term - I've been there many times!! :? Also, try to recruit your dp in helping so that you're not too tired. If anything, try stop using the car seat for sleep over a weekend. Also, try the sleep training during a time period when you know you won't have to take the baby out in the car for at least 3 days. It will really help if you let him sleep in his crib for several straight days.
Btw, do you think your baby may have reflux? I suggest using a wedge or something to bring the crib's mattress to an incline, which may help him sleep better.
HTH