This is the part that will not be amicable:

The better or for worse part.

Explain why it is she would be entitled to anything when there is literally less than nothing....or negative equity.

The marriage is over, you put it on the market and divide the winnings or losses equally.....its very simple.

If you want to enter into an agreement for paying on the home in lieu of child support............I'd consider that very much so for the ability to claim the interest on your taxes.
Study up on child support and what you can expect at tax season if you have a child or children by this marriage.

If you are feeling remorse, the game is over, don't. Time to move on.

I'm not an attorney, but you need to be looking at this a bit more objectively and remove the emotions in your equation to the division of assets........whether they are to the plus or minus.

Best wishes and remember, you may be able to afford it today, but tomorrow could bring another change and she might feel as friendly about cutting you a little slack....