I have not tried a drag bag, but he might prefer it since he's used to sleeping with you. Would your husband accept it, inasmuch as there could still possibly be some temporary odors if he doodles in his drag bag? If your husband is not complaining about odors, just the ick factor, then it might be the solution. It would be less laundry than a playpen/bassinet. With the playpen you will be washing doggy laundry every couple of days (no problem, you can even get a separate laundry bag to put it in till you are ready to run a load). You need ample blankets or towels for the bottom of the playpen if you want him to sleep sans diaper (good for the skin).
I like a playpen myself, but my dogs were not used to sleeping with me, so it was not an adjustment for them. However, if you do decide on a playpen, you can put it so close to the bed that your fingers touch the netting when you are lying in bed, and he'll know you're right there.
Have you tried expressing the bowel? He still may not be 100% doodle free overnight, but it helps. Tips on expressing the bowel are in this article.viewtopic.php?f=5&t=18586
Here is an example of a playpen with 3 pieces of linens. There's a blanket, a quilted bottom sheet, and underneath you can't see it but there is also a fleece pad. Every few days I have to wash to keep up. With the drag bag, you wouldn't have all that.