As for your concern that the round laying on the elevator can fall out of the ejection port if the 870 is canted on its left side, it really isn't a problem if you leave the forend slid forward just so it clears the loading port. Then the front so the shell is held in place by the extractor and the curved side of the elevator. Play with it, using snap caps for safety and you will see what I mean.
I like leaving the thing closed on a live shell with the magazine tube full. If the action isn't closed it's not locked. If you leave it in the condition you describe and grab it up by the barrel the action slides open ejecting the live shell.