My now almost 4 year old son had pretty severe silent reflux from after his early surgery onward (before that he never ate!). He has always been well medicated for the pain, but the physical refluxing has always disturbed his sleep anyway. As a baby he never really settled well into long naps, so he would take a lot of short catnaps throughout the day. One favourite position for napping, and for early night sleeping was prone lying up against us when were were lying at an incline of 30-45 degrees. For him what helped immensely was to instigate a really early bedtime, like around 6, so that he had a very long night sleep where he could really get some good deep sleep. He would wake refluxing and nurse, still does wake at night, but still he'd have a really long good deep sleep between the wakings. With that in place, he could cope better with the catnap schedule. Eventually he settled into having two naps a day and then one, as many older babies and toddlers do, but his daytime naps were always short ones.
Another thought: ds has always had problems burping, so our routine has always been to dance him to sleep (hold him vertically upright against our bodies and dance with him to music, applying gentle pressure to the tummy so all the gas comes out but no liquid with it, since he's vertical). This helps him to sleep much better. And at many stages we would have to get up with him at night and do it again, sometimes repeatedly -- I think he swallows air when he refluxes, in swallowing it back down, then does not want to release to burp -- or can't -- again because of the reflux. Even now I go in and sometimes he wants to sleep on his tummy on my tummy on an incline, and an amazing amount of gas comes out... We don't have him sleeping on an incline because it seems to be a really HIGH incline that he needs, but now that he's bigger he has several pillows in the bed so he or we can set up a high incline if needed. Often he just prefers to lie flat though. Lying partly curled up on his side also seems to help.
That was kind of rambling but I hope there are some helpful ideas of things to try.