[Christ]

Engine on, in any case, won't hurt the trans at all while coasting.

Ive done a good bit of EOC in automatic equipped vehicles, and never had any troubles other than software getting upset with me. The oil in the transmission doesn't just dry up as soon as you turn the engine off, and in neutral, there is very little load on the bearings, etc. so it's not going to instantly grenade on you.

Manuals, I've never hard tell of one that's not ok to coast in neutral, so long as its actually in neutral. You normally won't want to put a transfer case in neutral to coast... Many won't reengageeasily without coming to a full stop, and some require witch craft and potions before they'll go back into drive ranges.