Hey Preggo, just catching up. I'm glad Flaneur stopped by to give you a heads up on how it works next. It seems to me that you know the boundaries you want and any pseudo-logical issues with them that H are beside the point.
Your boundary is simple. H does not take her anywhere for any reason. I don't know her self transportation situation, but it seems to me she was able to get places her whole life before he came along (4 months ago as you say) so it seems hard to believe she can't now. The abortion issue is very tricky, but it is ludicrous to suggest that H's mere presence will cause it to happen or not happen. And, unless I am confused, the cost of it can be covered afterwards. Send him the biil.
But regardless of the logisitics, the important point is for you to say "H. Look. I don't want you taking her anywhere. It is one of the things you have to do in this process. It's a boundary. Logical reasons of why you should don't matter." You can tell him more if you want, but that seems like what you need to do. Boundaries are not a question of weighing pros and cons. They are there for other reasons.
Meanwhile, like everyone says, take care of that baby and the mommy carrying it. Physically and emotionally slow down and take time and take lots of relaxation.
Another thought, seems you said H came back carrying all the important things he didn't want to leave behind. He is been moving all week. How much "must have" stuff can be left? I think you may say "Look. Leave the rest for awhile and take a break. They're just things. If she throws them out or whetever, you can always get more. Forget about moving anything else until Monday (or whenever) and let's just relax together for a few days."