I was going to suggest a food puzzle and wham!!! you added that in at the end. Lucy loses interest in toys easily so I have a bunch that I rotate in an out to keep her somewhat interested. Antlers are a must. She like tennis balls too. She keeps one in her mouth and bats another one around like a soccer ball. It's really cute. Even though she is a 3 year old healthy girl she plays for small bursts and rests. Plays and dozes off, and so on.
It sounds to me that your boy has a great life and you are doing so much to include him in yours. Maybe he is still adjusting but it sounds like he is doing plenty of things during the day that he loves. From memory, he is an older guy--so maybe he just enjoys laying around. Also, I don't think he got really good care in his old house so maybe he just enjoys being by your side and having your attention. Doesn't sound like a problem to me!