I'm impressed with the choices you've made, and the honesty in which you are approaching this.
I'm gonna agree with both rotard and dyintorace, except d2r's math isn't so good. $1300 per month is $15,600 per year. Of course that's your take home not your gross, but still... As a comparison, a single full time minimum wage job would yield $15,080. Somebody is grossly underpaid.
Perhaps you have made a decision to be a single income family. Perhaps there are medical issues. Perhaps there are large amounts withheld for another purpose. I'm not sure, but you have done a great job of addressing everything possible on the expense side of the equation. You've gotta take another look at the income side.
It's obvious this has been a big burden to you. You can't let this whoop you. You are too early in your marriage to be under this much stress. So far, you've done good at keeping the priorities in line. But this is gonna start to hurt where it counts. Your family and marriage are too important to risk.
You've done a good job covering most of the details, but have not talked about your income. Your story is unusual in that most people under the stress you are under would have fallen very far behind in their bills, mortgage payment, and crashed their credit rating. You have not, so there are some things you have done very well, and some things we do not yet understand.
Help us understand some of the income decisions you and your wife have made.
If, for example, you have chosen to be a single income family, I respect that decision. I have made the same one. But in an age where household incomes are based on 2 wage earners, maintaining that choice means that I must earn the equivalent of not 1, but 2 incomes. That's not too easy.
I know you can't stand your neighbors. But if you could generate a bit more income, the financial stress of the house could be eased, and the neighbors wouldn't be as hard to take (for a while).
I'm concerned that your decision to foreclose could make things worse for you. A crashed credit rating, increased expenses with rent, etc. won't ease the stress.