OK, since the 'x' key is "broken" with that dragon (at least, only during that pose), I figured I'd fix the pregnant belly glitch by going to a werewolf and letting my char be defeated. That worked, and then came the moment for the explicit birth... Now, my character is stuck in the birthing position. You're also in 'masturbating' mode. You have to exit it and it's after going to talk to Isabel that it forced my char to stand again. No more pregnant belly...but now the menu to finish up/cum/show stats is always visible...
Edit: it turns out it's the explicit birthing that causes the invincibility (as well as the constant overlay for the sex interaction menu and the loss of control of the inventory--can be opened but you can't do anything there).
Edit: after sex with a Wilding, although you still have to open and close the inventory and exit 'masturbation' mode, at least the character is returned to normal walking and you don't have the sex interactions menu/overlay.