Alex B

This article pretty much sums it up. https://www.temple.edu/isss/immigration/overstay.html
Basically you shouldn't be here but under no circumstances do you want to be here after 180 days because then it starts to get increasingly ugly for you.
The ban seems to come with INA 212(a)(9)(B) which mentions the 180 days. However, 222(g) says that overstay cancels your visa and says that you now must apply for all visas in your home country. I suspect, but don't know, that this would make you ineligible for the visa waiver program.

The bigger problem here is #5 on your list!
#5 She's assisted in committing fraud and fraud is a crime of moral turpitude which is disqualifying for naturalization.

If you're worried you could also travel via Dublin or Shannon which are CBP pre-clearance locations.
Just bring lots-o-ties back to Blighty like bills/pay stubs/mortgage or rent etc. and you'll be fine.
Finally, make sure you have a copy of all correspondance with USCIS and later Dept of State to show that you're following the process to the letter.
You'll be fine. Just tell the truth, ALWAYS! Misrepresentation is the one thing that can be impossible to beat.
Remember, even if you are turned away it's because in the CBP officers opinion you are at risk of staying. Provided there is no misrepresentation it will remain just that, his/her opinion. Your K1 will not be affected. My wife was turned down for a tourist visa to the US once because she had insufficient ties. We disclosed this to dept of state and didn't even hear about it at interview. It was a complete non-issue.
Good luck.

For the rights issue I certainly was extremely uncomfortable with what happened after 9/11. This rights issue was one of the major drivers to my applying for naturalization. In reality the only time you could have a problem is if convicted of a crime for which the sentence could be more than 1 year. I seem to recall having seen some reports that they would even add up different sentences and deport people.
There is no automatic custody. It's down to each state. Here in Washington it's assumed that joint custody will be granted unless someone petitions the court otherwise. At that point my atty said I'd need psychologist reports etc. Thankfully my divorce was a very low-key affair without disagreement.
This whole needing a letter is a farce, plain and simple.
I've been divorced from my daughter's mom for a number of years. I do have a letter because we both believe that the one thing we want less than to be married to each other is the government messing around in our business. We state in the letter that it covers all trips for a 12 month period.
My experiences:
1) Canada - have been crossing the border every 1-2 weeks for about 2 years. Maybe 25% of these crossings I have my daughter with me so that makes about 12-13 crossings. I've been asked for the letter twice. Once I had it and no problem. Once I didn't have it and the Canadian border guard told me I "really should have it" and let me pass.
2) UK - Both myself and my daughter are dual nationals. The last flight we made back to London I asked British Airways if they needed something and they said they'd never heard of it. Of course, entering the UK we both use our UK passports.
3) Mexico - We've crossed the San Ysidro/Tijuana border on foot. You go through one turnstile to leave the US. Go through another turnstile to enter Mexico. One customs shack with a random inspection in-between. No questions, no asking to see the letter.
4) China - The consulate did ask for a letter, "but if I didn't have one that wouldn't be a problem".
These rules are just a way of punishing honest people. If I really wanted to abscond with my daughter it would be trivial. All it does is give people a false sense of security.

Yup. Me too on this one, in Seattle.
They took the card when I entered and went up to one of the windows. It was about 90 mins before I had something in my hand again. I was sitting there wondering what if the fire alarm goes off!

IIRC it's even worse than that. You get 50% credit for the prior year. So staying 100 days in one year, you're not a resident. Now you can only be in 130 days the following year before you trigger it. I got caught on this back in the mid '90s. I don't imagine it's changed.

I'm sorry for you. I'd definitely advise you to wait a little while. If you do nothing it doesn't hurt anything and if in a while you still aren't going through with it then you can catch it at the consulate. It would be terrible if you were to reconcile things and had already cancelled.
Good luck
Alex

Yes, it's meant to be carried, as proof of your immigration status.
I never carried mine (far too valuable to loose and a PITA to replace). Now it's not a problem because I don't need it anymore
I'd definitely carry it if you're anything other than caucasian and live in some state like AZ.

UGH! It all depends on if time or money is important to you.
The tube always used to take about an hour, longer if it breaks down on you (like the last time I went back to the UK). You should also look at the Heathrow Express but it's a little spendy at GBP16.50 for a single. I always used to use that when I was on business trips (aka on someone else's tab )