Finn, I'm sorry you're here, but I also know you'll get some great support and advice. I myself saved my own marriage from my wife's affair nearly six years ago, but we came VERY close to divorce a couple of times while everything was still going on.
I've followed nearly thousands of sitches over the past 7 years, and have personally counseled many people thru this. I've really only seen two approaches work, which I detail below with a copy-and-paste from my personal archives. I think you can do the "fight like hell" thing before the "letting them go" thing, if you want to save the latter in reserve, but if you think about it you really can't do the opposite.
Starsky (formerly "Puppy Dog Tails" and "Chocolateeyes")
Those are the only two things I've seen work. If #1 turns up nothing, then proceed to #2b. And in the meantime, GAL your ass off, and become the better option. Best case, you'll attract them back, and at a minimum you'll become a better person that will be more attractive to SOMEBODY in your next relationship.