The objectors' arguments are not flimsy, nor are they ignorant of visual concerns. Indeed they need to be resolved.
To remind you, the petition ends by stating: "If A303 widening at Stonehenge is felt to be essential it should be done by means of a deep bored tunnel at least 4.5km long. Anything shorter would cause irreparable damage to this landscape, in breach of the World Heritage Convention." This is consistent with the National Trust's former position, which very sadly they have abandoned.
The World Heritage Site is upheld by the World Heritage Convention principally article 4 http://whc.unesco.org/en/conventiontext/ which asks for financial measures to be taken sufficient to undertake the necessary improvements for the WHS even if it means an international appeal. If this Convention is breached due to permanent damage inflicted, then there will be a risk to the WHS status.
We also need to be aware that the recent Blick Mead discoveries are on the WHS boundary and might be vulnerable to more than just the tunnel. So the 4.5km reference might no longer be appropriate to properly safeguard the WHS.
True, archaeologists frequently rely on the opportunity afforded by development to piece together our past. But this is not the reason to build a short bored tunnel! It is short bored in order to save money and to restore only a portion of the Stonehenge landscape, ignoring the Outstanding Universal Value of the whole.
No doubt you will be aware that ICOMOS-UK, advisor to UNESCO, has written to the Secretary of State for Transport, warning him of the risks to the WHS.
Ultimately you, NT, EH and government, need to decide whether it is worth risking the outstanding universal value of the WHS.
Speaking for myself, I share the frustrations about the reluctance to do the best for Stonehenge WHS. The delays have not been caused by the objectors. If only Government had done the right thing in the first place and built a long bored tunnel as promised in 1994 instead of the distracting proposal in 2004 of a cut and cover that wasted huge resources, political energy and time, this conversation would not have been so prolonged and the costs would not have escalated to the extent that they have.
Something is not right. This message is just to keep things from messing up down the road