Hi K.,
I am a big believer in the cry it out method, but for OLDER babies. I can tell you from reasearch and personal experience that babies don't have the capacity to calm themselves until around 4-6 months, and even at that age, we only let our son cry for 5, maybe 10, minutes before going in and soothing him. It sounds to me like your daughter is getting worked up and it only escalates, as she can not yet calm herself.
I don't know anything about acid reflux, but I would reconsider your daughter's nap schedule, as it sounds like she goes to bed pretty effortlessly at night. Babies napping needs are always changing, and perhaps your baby needs either fewer naps, or naps that are more spread out. I would start by postponing her naps by 15 minutes from when they usually are, and then adjust as needed.
Do you swaddle her? My son loved to be swaddled. Swaddling with a blanket can be difficult, so we had a swaddler that had velcro and was very easy to put him in.
Another thing to consider at naptime is that your baby should be relaxed, but still awake, when you lay her down. Having a baby fall asleep in your arms is not the best habit, as they often wake up when placed in the crib, or shortly thereafter.
I would also try to ditch the car seat habit, but I know how easy it is to do ANYTHING to get them to sleep. I have read about special slings that go in the crib that sort of prop a baby up to a semi-sitting position. They are for acid reflux babies, and I personally have never used one. They might be worth investigating--maybe another mom who has used them will chime in.