Personally, I wouldn't worry about it too much. I remember we used to top up dinner at bathtime by offering porridge in the bath (which she loved!! lol). I was worried that I would end up having to do this forever, but she grew out of it. We also did bite, bite, sip, but we managed to do it with water rather than milk.
If it was me, I would be more interested in whether she is enjoying the food that she is having than the balance between milk and solids. At 9 months, food is still about tasting and experiencing rather than getting all her nutrients from it. As she and you become even more experienced with solids, I am sure you will spot opportunities to try water with meals or slightly fewer sips of milk per meal etc etc. I know lots of older kids that have a cup of milk with their meals - as long as the overall diet is healthy and balanced, I don't think the protein / iron absorbsion thing should be too much of an issue / an issue at all.
Oh, and if it was me, I definitely would have a cup of water available at every meal or a cup of very dilute fruit juice - just keep offering it and she may or may not take it but will probably take it and enjoy it eventually (might take months.... ho hum!). I would still have milk available at the meal, too, but maybe in a sippy cup rather than bottle if at all possible.
HTH a bit.