"I'd like to spend some time with D on her birthday. Could I drop them off an hour late and then let them stay overnight?"
Otherwise, just let D stay up an extra hour tonight. It will be OK if she is a little sleepy tomorrow.
XH is a procrastinator. You know this. Accept it. Don't fight it. Don't expect him to change or try to fix it. Do what works. What works is allowing D to get her project done properly. That it has worked out to be last minute is no surprise. Next time, plan on it, then you can avoid this problem.