Hi C.,
I don't know if this is a financial option for you, of if you job has any flexibility, but if so, I would see if you can cut back on your work hours some and take a nap somewhere before you get him from daycare/go home (however childcare arrangements are handled). I'm not talking about a long nap, but maybe just an hour of sleep before see him again - and you might be a little more refreshed to spend time with him. I'm also not talking about a long-term solution, just through the final weeks of pregnancy.
Another idea that came to my head was to see if you can switch to 4 10-hour days and get an extra day off to spend with him. I don't know if thats possible either, but something else that just came to mind.
Good luck with the delivery!