I'm going to try make this reply less harsh, but I'm having a really difficult time so I'll apologize in advance.
I'm the poly person in my marriage; my husband is mono. We have two kids (5 years and 1 year), my husband has a 50-hour a week job and no other time commitments outside our house at the moment. I am unemployed and in an LDR that re-started last August.
If he won't listen to you, then your husband needs to talk to other poly parents: having a baby makes it nearly impossible to have ANY time available for other relationships. Having a kid is HARD. He needs to man up and commit to you and the child he helped create. Whatever he thinks he'll be able to handle or manage, he's wrong. He doesn't have a clue, and he can't really until it happens, but he needs to approach the birth of his child with an attitude of, "I'll do whatever it takes for my child and my partner, and THEN, if it's manageable, I'll look at other relationships." If you and he reach that point before your child is a year old, congratulations. I reached that point faster after my second child (9 months) but there's generally a LOT more to get accustomed to when it's your first time around.
You're 41 weeks pregnant, fer chrissake! EVERYTHING in his world right now should be about how you and the baby are doing and what he can do to make these last (interminable) weeks as comfortable as possible for you.
Sorry, I don't know him, and I don't know you, but I have a VERY short fuse when I perceive a situation where the man (or non-pregnant partner) isn't doing whatever he can to lessen the burden on his pregnant partner. They can't help with all the physical changes, pain, hormones, etc, so they better be doing anything they can in the other departments!!
Pan Female, Hinge in a V between my mono (straight) husband, Monochrome and my poly (pan) partner, ThatGuyInBlack