I haven't had to clean my ML yet, but I'll give my $0.02 based on experience cleaning other weapons. I'd do the water thing like you stated and then dry. After that, use either a bore cleaner like Remington 40X or a bore brush with some RemOil on it. Then swab the bore until the patches come out clean. Then run either a pre-saturated lube patch like Remington Express Lube or a patch with some RemOil on it down the bore. That's it for the bore.

As for the rest of the gun... I'd use some kind of action spray on the trigger and other hard to reach areas. It'll blast out any left over oil that has collected any kind of dust/gunk. Once it has evaporated, mist it with RemOil from an aerosol can. Spray a clean rag with the same aerosol RemOil and wipe down all the external metal.

Soak the breech plug in some kind of solvent like Remington Express Clean Parts Bath. Scrub it with a tooth brush and then re-soak to wash it off. Wipe it off and let it dry. Apply some breech plug grease to the threads and reinstall.

That should do it.