I vote for Rumlow and co. being the world's worst labor coaches. Constant complaining about how long the whole thing is taking. When the Soldier's water breaks, they make him clean it up. Same when he vomits during transition. They put him in stirrups for a while, just so they can get a better view, but then it gets too gross even for that and he's told to go sit in a corner for a while. There's a particular strain of humor that shows up in some STRIKE-themed trash fics that actually just highlights the humiliation and cruelty of the Soldier's life and it could work very well here.
Re: mpreg, graphic birth, body horror, DEAD DOVE DO NOT EAT