Puppy with broken leg

Our puppy broke his leg 2 1/2 weeks ago when he was just 12 weeks old, and had to have surgery. For the first 2 weeks we had to keep him confined to a crate almost exclusively, which we did. We were able to take him out and hold him when he was sleeping or very calm, but if he started to jump around it was back in the crate. Now the vet says that as an alternative we can tether him to something heavy and keep him somewhere where he has a very small area to roam, as long as that area is carpeted. We've been doing that for the past few days, moving him from room to room with me as I work. He gets a lot more physical contact that way as opposed to when he was in the crate. However I just read an SPCA article on how bad it was to keep dogs tethered for long periods of time, and now I don't know what to do. He seems happier on the leash than in the crate because people are always petting him and interacting with him. That's kind of hard to do with him in a crate. But I don't want to hurt him socially. I have 4 more weeks before he can run around, and I'm agonizing over how to best care for him during that time. The vet has given me plenty of advice for keeping him healthy, but I need to know how to best keep him happy.