The only "practical" option that I've used on smaller outboards is to hoist the engine up with a lift mounted on deck, but out umbilical isn't long enough to clear the water; and even with a 115 HP that was not the easiest, but it did work. I have seen boats where the outboards are on a jack plate, and the lower unit, vertical, can be out of the water, but that's not my tugs either
I'm not giving up yet, there's a way but it will never allow the water pump replacement, that's gotta be a haul out.