"They used to get around this by venting the hydrogen at a proportional rate so the flight remained level."
Later airships captured and condensed the water in engine exhaust in order to maintain trim.
"However due to the expense of helium, this isn't really considered an option these day"
If you have a compressor onboard you can pump helium (or hydrogen) into (relatively low pressure) storage tanks, taking it out of the gasbags. This has the same effect as chucking it overboard without actually chucking it overboard and means you don't need to faff about with complex condensing kit in a hot gas stream.