Nice simple idea, though just needs something to make it that little bit more interesting without spoiling the simplicity.
As has often been pointed out here though the BBC TV channels at least desperately need their presentation tidying up and somehow unifying once again while enabling individual channels to have some kind of identity of their own - and the one thing all the channels have in common is the BBC blocks, so using them as a key component for endboards and cross channel promos makes a lot of sense.
I really do love this mock even from just the few things you've shown. This could be a great way of tying together the presentation of every channel without having to spend money on a complete rebrand for each of them.
I like the idea of re-branding the BBC channels, and I think this would be the right way to go. It makes the whole brand look 'neater' and could easily work on screen. Well done.
This was the next idea I was playing about with. It's for a now/next/later slide on BBC One. However, I think this is a bit too complicated for the branding I created. I might tone it down a bit in future.