What would your corrective training be in this situation?

A few choices, first I like to keep things out of record books (career killer crap) when appropriate. I would roust the two out of the rack and have them "escorted" them to the PT field by any number of capable NCO's. They would participate in the PT run to the end of planned activities, then we would discuss the 0400 sign in. What about the missed 4 hours? Personal counseling sheet on both personal: 1) appointed place of duty, 2) partying on leave is okay, but not to the point of not being able to toe the line for formation or work schedule, 3) missing your 0000 sign in is considered UA (unauthorized absence). I would suspect that the reason he did not sing in was because he was to intoxicated. Any further occurrences will be forward up the chain of command for appropriate action at an Article 15.
The Master Gunny would like to take these two on a little run to the top of Margarita Peak at Camp Pendleton. They might leave a puke trail for you to follow. Semper Fi,

Possibly an Article 15 (it's not always that cut and dry). I do not believe it's hard to correct integrity - it's our jobs as NCOs to do just that. As a Sr. NCO we are taught to take everything into account and provide counseling specific to the infraction. These counseling sessions would not merely be focused on the traditional "corrective training opportunities", they would also include heightened awareness of how these infractions damage the very fabric of the team. I have on several occasions selected movies and books which illustrate these areas, have the soldiers read/watch, and write an essay on the actual subject. As an Infantry Drill Sergeant - be assured - there would also be physical actions as well. Depending on the solider's past infractions there could be many creative variants of physical actions (ie soldiers lead every PT session for 2 mos - xtra duty etc.) and intellectual ways an NCO could deal with this situation. Just remember, slapping an Article 15 on a soldier is never the extent of an answer - an NCO must lead by teaching, not just punishing.

Honestly, you've been put in a hard spot. You have 2 options to go. Official paperwork, or in house paperwork. Personally I prefer the in house approach because if they don't straighten up the first time, you can go straight up the chain of command with official paperwork. I definitely agree with Master Guns. It's your place to tell them where to be, not their place to tell you whether or not they show up. So I'd show up on their doorstep an hour before PT is set to start to make sure they are up and ready. It sucks for you being their NCO, but thems the breaks in a leadership role. I don't understand why he signed back in late. If it's after working hours, he still could have signed in and enjoyed the rest of his night. If his flight was delayed which seems like the lie he's trying to use, then he should also be aware that he's supposed to keep his NCOs in the loop regarding any change in travel plans/flights delays etc.

It's not your responsibility to make sure he gets a full nights sleep, it's his. And his mismanagement of his own liberty/leave is going to force him to suffer the consequences. Then you should tell him that you are aware of their lies and punish accordingly. I don't know if they're repeat offenders. But they should be made aware of the seriousness of their actions. Document everything because like I said, if they step out of line or mouth off or whatever, then you can just put it in the command's hands and wash your hands clean of them.

You can't be their buddy in this though. They need to know they are being punished.