Andro
That sounds absolutely horrendous, so you have my complete sympathy!!
In your situation, I think there would definitely need to be consideration, but it's obviously difficult when it's a crying baby, and not much the parents can do about it. (Other than apologise, which as you said is nice, but won't actually stop you feeling pain and discomfort)
It's a tough one, I think give and take and consideration of people's situations is definitely needed..
I'm quite shocked tbh, I'd have thought that something so obviously affecting your quality of life would make you eligible for some kind of funding, free sound proofing or something
I was very lucky with my neighbours when DD was a baby and I lived in a ground floor flat. She was very colicky, with reflux, and had as of then undiagnosed cows milk allergy.Upstairs had 3 kids of their own, so noise from kids didn't bother either of us, and next door flat was an elderly man, I would say through half opened bleary eyes 'Sorry if you were woke up last night, she's not been well' and he would lie and say he didn't hear anything.
My neighbour after that though, was a self entitled prick, and constantly complained about everything.
I had a trampoline in the garden, and when they would bounce on it (in the daytime) and run around playing and making normal kids-in-the-garden noise, he would flip.
Made me really anxious, and I felt like DCs couldn't enjoy playing in their own garden, as his head was always poking up, telling them to be quiet. He would come and knock at the door and complain about everything, but only when DPs car wasn't parked outside 
When I moved to my current house, it was a few days before I saw the next door neighbour, and I said sorry if you have heard the kids running around shouting, they've been a bit over excited about the move, new bedrooms new garden etc
Neighbour looked genuinely baffled and said 'I've literally only just realised you have littluns, I haven't heard a peep'