i am probably opening a can of worms here chocospence, but my dd has had reflux since about 3-4 weeks old and was unmedicated until recenty. She is now 4.5 months. since the reflux hit we could never get her to sleep on her back, we had to rock her in our arms whilst she was on her side IYSWIM. then we could transfer her to her cot, but this wasnt always successful.
(this is where it becomes controversial) She sleeps on her tummy and has done since 6 weeks old. After much terrible worrying, and almost no sleep i came to the conclusion that 1) there is an elevated risk of cot death, but how would i ever know whether she would die anyway, or whether this was tummy-sleeping related, 2) she is in the bedroom with me, and 3) i would die if i didnt sleep soon.
She sleeps on her tummy, and i would do it again in a flash. She is strong, and able to rol over easily, she knows the difference between bed time (on tummy) and play time (on back). she sleeps soundly from 7pm-10:30 when she has a dream feed, and then 11:30 until about 6 when she'll nap on and off until 7.
obviously i cant say whether this would suit you lo or you, but i just thought i'd outline what works very well for us. Having said that, after 4 months of tummy sleeping, dd will not tolerate sleeping on her back, and struggles to sleep in a car or pushchair because she wants to roll over and cant. So i couldnt guarantee that even if you wanted to try it, your lo would comply!
have you tried elevating her mattres so her head is higher? this helped my dd a lot when she was small as it helps reflux symptoms.
good luck