Really nice mocks Jonny - these made me smile!
I'm fond of the 1991 era, and have always preferred the look of Futura over Avenir, so there's a lot about this that I like - particularly how the Next device has become a form of programme slide!
Just a couple of areas to perhaps re-visit - making the stacked BBC2 logo in corner slightly larger; and on switching between solid '2' and outlined '2' on trails, to stick with just one of those two (personally I would go with the solid '2', but if it really has proven to be impractical , then it would have to be the outlined).
I suspect you may have already tried taking design cues from the 1991 slides? White logo as in the trails, and have the vertical strip background containing the ident-themed design instead of the '2' itself. For reasons of consistency I would say that would be the better option.
Now, this is really just nitpicking, but something seems off about the BBC logo letters; too angular I think. I can't say for sure at such small sizes, but it looks that way - so it depends on your source. I recall the 1991 logo included in one of the online TV font packs didn't have the letters quite right, so if you have used that version then I guess that's understandable.
Lastly, I really approve of the idea of recording these to DVD > VHS as shown in the video - I've tried it before very roughly of course, and it's good to see you giving it a go too! Aside from giving it a layer of authenticity, recording to VHS lets you know how the design holds up to reduced resolution and merging of the colour/brightness information - an excellent idea all-round.