My nobhead woke me by barking in my ear at 4am so feeling fairly strung out myself...
Regarding scatter feeding, as several of you have said, it's really down to the dog.
Bill struggles to settle on his own - he could do it as a puppy but has struggled since adolescence, and needs my help to regulate; and, because he's working lines, when his levels of arousal go up, they can go stratospheric, so I'll take anything that can help him slow down, like sniffing, shredding, licking etc. And he loves hunting and sniffing. So usually at least once a day I'll either build him a game from recycling, or I'll use a Nina Ottoson game, or I'll do a licky mat. They also have the advantage that when he's being a diva about eating his food, he'll still eat his kibble from out of a bloody toilet roll - and even his flea and worm tablets, which he won't touch otherwise.
I don't have a lawn but I'd totally scatter treats for Bill if I did. We play find it all around the house with treats, and I use it to distract him from other dogs sometimes when we're out, etc. It's a fun reward for a sit/stay if we're training, too. I'm also very happy for him to take treats from other dog owners - I really needed him to be at least passably sociable when he was tiny as I knew he would go to daycare, and if I couldn't talk to other dog owners I wouldn't talk to anyone some days.
But again, this is all about me responding to him - he's not always an easy dog, he's got big feelings, and he needs a lot of me and some help sometimes to manage the world. Mind you, so do I 😄
PS if I got another dog I'd definitely be looking at a GR - hard to believe one could be more demented than Bill and every GR I know is a wiggler, which is absolutely heart-melting.