Hi A.,
It sounds like you are trying to do a lot at once - and with a very young baby. What is most important to you? Moving out of the bouncy seat into the crib? Sleeping longer? Moving out of the swaddle?
I would think that you can't really make any of these changes until you are sure his reflux is really under control. Once you know that, then I'd choose one of the above things to start on - probably moving out of the bouncy seat for safety reasons. Once he's sleeping in his crib and not in the seat for a few weeks, then work on moving away from the swaddle, or whatever is next on your priority list. But too many changes all at once it bound to be upsetting for a baby.
Also, I agree with another poster who asked why you are making him wait so long before feeding him at night. That is a very long time for a 4 month old, even with the cluster feeding earlier in the day.
I can't comment much on CIO method, because I never did it - it just didn't feel right to me.
Best of luck, and the most important thing to remember is that this is a phase. Sometimes it seems like the nights last forever when you are tired, but they don't I promise!