Nothing to do with the mock but I've just realised how much Reith Sans looks like it should be on a packet of hay fever tablets.
I think you need to take the brand a lot further away from BBC News. Whilst Liquid News was made by a BBC News production team, it wasn't really branded as BBC News, and its graphic look wasn't really related to the wider BBC News look at the time. There was a short cut-down show that aired on News 24 each week, but that was about as close to 'News' as it got.
I suspect the 'Liquid' of its title would still be visually represented somehow visually.
BBC Three News (aka The News Show / Seven O'Clock News on BBC Three / 60 Seconds) was then a separate News brand of its own, and also not tied into the whole Gill Sans BBC News look at the time. If it were still around I suspect it would be closer to Newsbeat branding than BBC News Channel / BBC One/Six/Ten branding.