Well we are past a month now and I have been doing dairy free with Erika for her constipation and it hasn't really had that much of an effect. Which is a bit disappointing, however it has the advantage of only 2 varieties of milk in the house instead of 3.
Now she seems to be doing a poo every 2 days, and it isn't really that hard, though it still seems to be 2-3 on the Bristol stool scale.
I have been adding extra virgin olive oil to her breakfast cereal with bran and hiding it with extra sugar and she seems to eat it quite well. I doesn't seem to be harming her and from what I can tell it doesn't cause dependence either. I wonder if it's bad to have it every second day which is what I've been doing for her.
Edit August: It has actually improved her constipation a lot! And it works quite well, so I'm pleased. I have read that olive oil is a natural laxative, and has antioxidants so that's good. However it doesn't have any omega 3, which you can find in linseed oil (flaxseed oil). Maybe I should try that instead (though it is a lot more expensive)