Hi Emma,
Just wanted to tell you about something I was told by a midwife here.. If baby is refusing one side you can try to trick her by first putting her on the preferred side and get the letdown going, then quickly break the latch and move her to the other side without turning her round. So you start in the cradle position on the right, then slide her across into the rugby hold to feel from the left. Sometimes they don't really get that you switched sides as they are still facing the same way. Was told this works very well for most young babies that are refusing a side. I guess you could also start in the rugby hold position and then switch to the cradle , if that feels better. I've not tried this myself as never had full refusal but it sounds worth a go.
Sienna definitely prefers the right which has a bigger supply and stronger letdown, and I remember that in the very early days (sort of first 1.5 mos) she did prefer the left as I also had slightly OALD.