Hi Boo
Just wanted to add from a professional perspective as I work in post adoption support. I would absolutely heed against making an approach at this stage. We find that it's much more likely to end in tears for all concerned when people take matters into their own hands.
Re letterbox contact - perhaps you could approach the LA concerned about reviewing it if you would like it more frequently? You do have the right to do this, although it will be up to the adoptive parents to agree to it, hopefully they would discuss with your birth child before making a decision. I would also suggest that you write a letter to go on file for her, as if she does decide she wants direct contact when she is older, it's likely that she will access her adoption file first, and something that outlines your thoughts and feelings honestly about why things happened as they did back then, and how you feel about contact now, is likely to be helpful. You can be supported to do this by referring yourself for support to whoever provides adoption support in your area, it's usually an independent agency and not social services/the adoption team.
However tempting it is to pursue this at this time, for the sake of your daughter and for any future relationship you may have, please don't. Thirteen is an incredibly sensitive age and we find that for adopted people especially, adolescence is tricky and tends to be a time when their adoption can throw up lots of complex emotions/issues. The likelihood is that she won't be mature enough/ready for this. You would really risk causing her a lot of upset and distress, and the fallout would be detrimental for you both - you would probably lose letterbox contact, leaving you with nothing, and everyone would be much more wary about promoting contact once she is older. It's very unlikely that this would have a happy ending, quite the opposite, you would probably end up in a much worse position than you are now.
Try to focus on the positive. You have some contact with her and can ask for more (some adopters refuse to engage in letterbox at all, leaving birth parents knowing absolutely nothing). Also, your daughter may be curious about contact (girls/women seem more curious about birth family and seem to tend to explore contact sooner than boys/men - purely anecdotal) and so there is a small chance that in the next few years she may want to know more about you and if her adoptive parents are supportive then this can lead to more contact, with involvement from adoption professionals for all parties. And if not, when she is 18 you will be entitled to ask for an intermediary service whereby contact can be made with her on your behalf to see whether she is ready for it. Even when she is 18 you should use this approach, whether you know where she is or not.
Please sit tight and do this properly when the time comes OP. I am sure it will be better for you, and most importantly, better for your daughter. I am sure that her welfare is your main concern. It's a waiting game and must be so vey tough for you, but remember, we are adults much longer than we are children, and hopefully you will have many years ahead to be able to get to know each other slowly and appropriately.
All the best x