Gwylan, yeah thats a good route. funny we forget entire lines exist. I'd still want to avoid the warren that is London Bridge underground, wouldnt fancy with baggage and group to corral. the Tower hill change is simple.
if you're going to London City, presumably on the DLR, you want to goto Victoria, get on the District/Circle to Tower Hill then the DLR. it might look a further but its easy inter-connections