To add to what you've said so clearly,VBB -
VBB, to add to what you say:
So far as preserving or learning about the two tunnels is concerned, the ICOMOS/Burra principle is relevant, since it would be what would need to be invoked:
"The traces of additions, alterations and earlier treatments to the fabric of a place are evidence of its history and uses. These will often be a major part of its significance. Conservation action should assist and not impede their understanding. "
To my mind, the application of this principle is a matter of judgement and balance, and boils down to case-by-case common sense. Perhaps Littlestone will elucidate how its equivalent is applied in his own field. But in the case of the Atkinson tunnel we have a fifty year old partly collapsed badly executed and poorly documented tunnel constructed in connection with a telly programme, in the heart of a 4,500 year old Neolithic mound. Whilst the Burra principle makes good sense in the case of the successive alterations to an Elizabethan Manor House, it makes little sense in relation to this tunnel. That alone ought to be a conclusive argument against spending money we don't have on it, I would have thought. But if one then adds the fact that it seems it can only be studied or preserved at the expense of vast additional losses to the original Neolithic archaeology then it becomes an absolute non-starter. Better to rip up the conservation manual, avoid philosophical navel-gazing and listen to what the untutored public, the true owners of the monument, will say: "don't be so ruddy daft."
If that's not persuasive, consider what our great grandchildren will say: "So you caused huge damage to the original, so you could leave us with knowledge of a twentieth century tunnel, did you?"
If the tunnel goes ahead on the basis of wanting to learn about or preserve twentieth century meddling it will be on the basis of grotesque misinterpretation of internationally recognised conservation principles. But that's already perfectly well known, of course.