Congratulations on selling the house. Mine will have an inspection on Saturday and I'll hopefully out in February.
And it's fantastic that you found such a great place out of walking distance from where your former spouse runs out of gas. That is great planning on your part. And it's beyond weird that someone runs out of gas so frequently.
I'd suggest that next time you come across something that is hers, reminds you of her, toss it. Drop that emotional connection. It's like showing her a major booboo which she doesn't and won't care about when you put in a box for her to take care of.
The end result of a divorce is more about taking care of the kids than nursing the hurt. Grieving is a good thing. Wallowing not so good.
All I know after reading your threads is that you're a very good guy, intelligent and nurturing and excellent in your profession. And a great father... a gift beyond compare.
To paraphrase Bill Clinton immortalized axiom, "it's the now, stupid". Something for me to remember, too.