Dont introduce / re-introduce anything (including the baby when it comes). Anything that hes previously grabbed at is of no issue now. In fact I wouldnt allow any free roaming of the house. I would remain silent on the days you allow him in - its a huge honour for the dog being welcomed into the pack leaders den. Always lead him in when you welcome him in and only when hes most calm so he remains in that state once inside, this sets him up to not being excited and needing to use his mouth. If he has a future bed/place/rest area planned, set up a old towel - it will smell like you both and he may choose to settle there. (my dogs did). Then reward with a high value treat in that place... a dental stick or such is good as it will encourage calm, and calm gets rewarded inside.
If he enters calm and everyone remains calm he'll always understand that the house is for calm and outside is for running etc. This will be perfect when youre busy with bub. Once bub arrives you can add a clothing item from baby to his bed area by way of introducing him to the new pack member.
I'm honestly a little bit confused - don't introduce anything? Like... Just keep everything away every time he's loose?
Maybe I didn't communicate his living arrangements clearly. He does come in every night and when necessary due to weather, he sleeps in our living room in his crate. His crate is his only "Place", which he only knows as "Crate" and he is happy to be there. He is only about ten months old, so very much still a puppy. He is a GSD/Golden 50/50 mix, so he's got a good long while yet to grow and mature. He very rarely uses his mouth at all now except in active play on toys or when he wants to try and interact with something interesting, so I'm not concerned about that, because he also listens to corrections pretty well for that kind of thing.
When putting him out and bringing him in, he sits while being leashed, then he's given a command - "let's go outside" or "let's go inside", which he knows means going to the back door. Then he sits again, the door is opened, he waits, then we go "Through" the threshold. He sits again and waits while the door is closed, then he is either given the "Crate" command, or he is walked to the dog yard depending on whether he's going in or out. Then he is unleashed either in the crate or after being put on the cable, and settles by himself.
Anyways, the general idea does match the rest of what you said. He was led into the house by my husband, worked with a bit until he settled, then released. We didn't do anything out of the ordinary, just walked and sat around and pet him etc. as if it were a quiet evening at home. Only difference in the house was that some things were missing, and the chairs were blocking some plants.
Now, he never enters the house in a calm manner.

That's what we're working towards. He gets very excited to do what he's asked and he does things extremely enthusiastically. Neither of us give him energizing body language when he is inside. It will take him a while to calm in general, I think it's mostly a maturity thing, but we are working on it when we can nonetheless. Ah, and we don't play with him in the house. There isn't enough space to do that anyways, haha.