I'm sorry you're going through this man, I really am. As far as breaking her out of the fog, I agree with the others that there isn't anything you can say in a letter that'll do it short of filing for divorce. My wife was pretty awful in the weeks following my discovery. I did the pick me dance hoping to find the right words or actions to snap her out of it. None of it worked.
It wasn't until I started calling divorce lawyers and set up consultations right in front of her that she broke down and snapped out of it. She went from being awful about it to begging me to not go through with it almost immediately. That was the beginning of the end of her affair. Before I did that she insisted on maintaining a "just friends" relationship with her AP. A situation I just couldn't tolerate. After I made those calls she broke down, literally begged me to not go through with it, sent a no contact message, blocked him on everything, put in for a location transfer at work (AP was a co worker), rolled her sleeves up and began the hard work of repairing the damage she'd done.
That was just about a year ago today, and she's been a model for reconciliation since. I'm certain she's stopped all communications with her AP and actually hates his guts now. If it weren't for her infidelity I'd daresay we have an almost ideal marriage right now, but it did happen, and at a year out I'm still having some rough days, but she's weathering the storms and really sitting with me in it. It's early days still, but if we continue on this path I really think we're going to make it and come out of it stronger than ever before.
That was my experience. To snap her out of it I had to show her I was willing to end the marriage, and from what I've read that's generally what it takes. Turning up the "nice," tip toeing around, and trying to spare a wayward spouse's feelings just doesn't work. You can't "nice" them back. They need to see consequences, or potential consequences.
Now, I also know from being on these forums for a year now, and having read many more stories that I ever wanted to on this subject, I know that my wife's reaction isn't the norm. She's what some would refer to as a unicorn when it comes to these situations. Rare is the WS (wayward spouse) who snaps out of it so quickly, does such a drastic turnaround, and still sticks to it a year later. Backsliding, lying, taking things further underground, continuing to blame shift, and continued deception is unfortunately more the norm.
I have no idea what your wife may or may not do if you follow my tactic, but I do know that almost nothing else works. If there's any kind of chance to salvage the relationship thays what usually does it. You have to take a stand and show her you won't tolerate it anymore. If you do start the process, make sure you mean it and you're ready to follow through with it if she calls your bluff. Backpedaling will just blow up in your face, so be prepared to follow through if you start it. Unfortunately I think that's really your only option unless you're prepared to continue living in infidelity. I came to the conclusion that divorce is a better option than living with that.
I'm sorry you've found yourself here. I'm sorry we don't have a better solution for you, but there is no magic phrase or action that will change a cheating spouse who's wrapped up in the dopamine high they're getting from an affair.