I always wrapped both of my kids up in a good wrap (I love gysymama, but many people love moby, which is a bit cheaper) and wore then in that throughout the day, tummy to tummy. It seriously worked wonders for their reflux!! It allowed them to feel warm, safe, and close to mom, but also kept them upright, which is huge. They would both nap really, really well in it! Plus then I had my hands free to cook, clean, play with siblings, etc.... I totally agree with you on not letting them cry. I wouldn't let my babys anyway, but ESPECIALLY with reflux. I can only imagine how much pain that would cause. I read a wonderful book that I highly recommend. It's called the No Cry Sleep SOlution by Elizabeth Pantly. It is a LIFE SAVER!!! You can get if from amazon.com, the library, or on her website, just google her name. Good luck!
Also.... we took both the kids to Dr. Kirk Van Metre. He is a chiropractor with four girls of his own. It really, really, really helped. Between the wrap and him, I never had to mediate them.