I stand at the opposite end of the spectrum, in that I've recently left my family (18 then, 21 now), and don't plan on ever returning. The only difference being that I've actually confronted them.
While I think your intentions are in the right place, I found myself growing increasingly angry as I read your letter, particularly this part:
Seriously? Trying to gloss over your problems and take credit for her running away is NOT HELPFUL. I guarantee that if she reads that, your chances of reconciliation will plummet even further. If you really want to reach her, you need to be relentlessly curious about why she ran away, why she isn't interested in communication.
Looked at another way you could say I’d very successfully reared a chick that was ready to launch itself onto the world without a backward glance! In fact you have been independent for nearly two years now, no mean feat in the current economic climate!
Your letter is entirely devoid of humility. You don't even acknowledge that there's the slightest possibility you may have done something to hurt her. You seem to want to chalk it all up to individuals having their mutual differences, when you know damn well that's not how the parent-child relationship works!
And then you finish off the letter with an ultimatum??? Your daughter leaves you, makes it very clear she has no interest in seeing or speaking to you, and you're STILL trying to dominate her into doing what you wish? This is also really, really not helpful, to your cause or hers.
However, this is the last time I can help. I want that to be clear. I want to work alongside you during those 9 days as equals and then let you get on with your life whilst I get on with mine.
Think about it: good marriages don't end in divorce. Likewise, children don't flee parents who treated them well.
If you want your daughter back, you need to ask questions and listen. Stop trying to control the relationship.
“The whole concept of a macronutrient, like that of a calorie, is determining our language game in such a way that the conversation is not making sense." - Dr. Kurt Harris