Hi Cass, welcome to the forum!
This is a tricky one and not at all uncommon as far as I can work out. While putting your baby to sleep on her back substantially reduces the risk of cot death as you will know, it also seems the case that many babies prefer to sleep on their fronts, maybe because they feel less exposed that way.
Does she have problems settling or is it that she wakes herself up?
When on her back does she wake herself up and wave her arms and legs around? If so have you tried swaddling her? She might prefer to sleep like this anyway as she might feel more secure (but be prepared that she might not like it at first).
Is she sleeping in the same room as you? If not then keeping her near you might also help her to settle.
If I were you I'd persevere with back and side for a bit longer because of the risks. I know that's easier to say thatn do though, some babies just hate sleeping on their backs.