I have only had one other puppy, so my frame of reference is very limited. That puppy, however, did not go through any kind of "fear period." I didn't know that was a thing. How long do fear periods usually last?
We've been doing suggestion #1 all along, and will continue to follow that guideline. That said, his fear of inanimate objects does not appear to be going away now that he's 4 months old. We have noticed, however, that he's a bit worse when it's raining outside.
We'll try to incorporate #2 into our walks. Unfortunately, we live about 3 blocks from MSU campus and very close to downtown East Lansing. Many pedestrians are on their way to or from class or work and aren't interested in petting/feeding/walking a dog. Maybe it is their backpacks/work bags, or the purposefulness of their walk that frightens him. We also live in an older neighborhood with a small yard. Other people are always close.
He is improving around other dogs. We have gone out of our way to meet up with other dog owners at parks in our neighborhood so he can meet other dogs and play. We go almost every day, and I think he has really improved in this area.
I'll be sure to work on getting him used to being uncomfortable while being handled, too. Unfortunately he is a very mouthy dog altogether. He has ruined a lot of clothing (along with deck pots, shrubs, downspouts, hoses, sleds, toys, etc.), and our younger two children are not allowed to be around him unless mom or dad have him leashed... and even then. We have been working hard with bite inhibition since we got him, and he has improved a bit with my husband and me, but he definitely can't be trusted around young children. Even with me he can be "careless." He's especially bad when having the leash put on or taken off, and his bites frequently break the skin now.
We'll keep on keepin' on, but at some point - if he has good character - he'll turn a corner... right? At what point do we need to seek professional help or assess our options?