Regarding your "testament" I wonder how many people in the world would have the training and experience to provide the level of detail you're demanding. From what I gather the whole "question" appears very much to be set up only to be followed by new constraints regardless of the answer.
Let's say my drawing for Oxford Street (IIRC you've brought it up earlier) would be to make it pedestrianised with cycle tracks I'm almost sure there'd suddenly appear new constraints I'm supposed to solve rather than you attempting to find a way to work within the constraints of Oxford Street being pedestrianised. I might be inclined to have a go with some back and forth but the way your question appears to be loaded demanding nothing short of world peace as an answer I'm not entirely convinced it would be worth the effort.
you'd have to do what anybody else would do - justify the design. I suppose it's no different from me having to justify a design for a building (which can be a heartbreaking business), but, given that the 1:1250 map and streetview would be able to tell you all you need to know, then you might give it an honest go - as I did for the stretch of road in Islington. You would then, I suggest, come to the conclusion that it's more difficult than it is in some beknighted suburban grid like Groningen or Milton Keynes.
Having said that, Oxford Street isn't where I'd start. Traffic is pretty much reduced to pedestrian speeds and they're widening the footpaths as we speak to make it, in essence, one long bus queue. Pedestrians cross the road from shop to shop, and from shop to bus stop. My suggestion would be one of those arterial roads that have not taken off in the manner of the A3/A24, the A10 or the A200. The A404 would be a worthy test - it's an important arterial road, and links one suburban centre to the next
Or the Stratford Road in to Birmingham - which is genuinely about the best chance you've got that I know of. I couldn't possibly deny that there is the room - but I'd contend that it was entirely undesirable. If Birmingham city council had any gumption they'd stick in bus lanes......
Or the A68/A7 Dalkieth Road in to Edinburgh.
to return to the roundabout. Each of these arterial roads have a mix of uses. They are places in which people recognise themselves, although the Stratford Road example is clearly very different from the Harrow Road or the Dalkieth Road. They have scale. Their problem is that they are beseiged from within by the motor car, although if there was any place in which the motorcar would be acceptable I suppose the Stratford road would be it. David Hembrow's representation of Groningen is of a suburb utterly given over to transport. It may be efficient in terms of getting people from A to B, but it reminds me of the civic desert that is the Midwest town (with roundabouts).