Seems like dropping the chains because of cross-chained on the small ring will drop off the outside, between the rings. OP gives me the impression that it's dropped to the inside, which would need a really bad chain-line to happen on the small ring and big cog (ie, not cross-chained).
So I wonder if his DR cage is just out of whack, or the hanger. Bent inwards.
ps, it would be a little silly IMO to insist on picking the bike up every time you want to move it backwards, out of fear of exceeding the design capability.