Have you been over to the reflux board, there is a lot of experienced reflux moms over there.. i would post your car seat question there.
Do you have the reflux under control? Tracy would say we fix the medical issues before moving forward w/ sleep training.
It could be the postion of the stroller vs. the crib (do you have it elevated) or the motion of the stroller feels nice to her...?
I am not an expert on reflux, actually last week the ped allergist said my dd might have it and it went untreated for 14mos! Would you like me to move your post to the reflux board and we can see what those lovely ladies have to say?