How to move the body of someone I killed theself

MJ12

MJ12 are semi-ordinary human beings. I can confirm Albort's comment about the baton: in my non-lethal play-throughs I've taken out MJ12 with the baton and the strength mod. Possibly without the strength mod too -- I don't remember for sure.

You might want to try crouching and hitting them in the knees from behind: I know for sure that's more effective than a back-hit for the riot prod, and it might also be more effective with the baton. I believe head hits are more effective too. You probably know this, but the key is to catch them by surprise. As soon as they're alert, a nonlethal attack does way less damage.

You can also take them out easily with tranquilizer darts.

MIB

MIB are another story. The only non-lethal way I ever found to deal with them was to avoid them, or to take them out with tranquilizer darts. And boy, it takes a lot of darts. Also, it's been a few years, but it's possible they explode after falling unconscious... not sure about that.

As for a one-shot non-lethal MIB takedown: while I haven't obsessively tried every method (and this from someone who had obsessively played through the game eight times :-), I don't believe it's possible. They're incredibly tough.

Seems there is no reliable and reproducible way of getting past this. I did it on multiple occasions, where I threw things around and snuck past the guards behind their backs, the whole time crouching.

They sometimes detected me, and at other times just minded their own business.

At one time I took the left corridor, threw a small glass item to the right when I reached the mid part, then sprinted off to the finish. So stealth is not the only option here, and I think that's the message the game wants to deliver: there are always options.