1.7 Billion ... for a couple miles of tunnel? Through/under green fields? That is an insane amount of money.
Put down some gravel and pave a road. Any artifacts will be safer under the road than if dug up for a tunnel. If you dont want to see the road, box it in above ground. Plant hedges around it. Dont rip up history just because you dont want to spoil someone's view.
There already is a road there. That’s the whole point. It’s one of the busiest in SW England and it is only ~200m away from the monument. The whole area (I.e. the “view”) is a protected historic landscape and it is blighted by the road. The plan is expensive because it is a bored tunnel. It is where the entrances of the tunnel are that is controversial - the middle of the tunnel will be deeper than the archaeology.
On a weekend just have to avoid the road there. Yes it is busy but what makes it so awful is everyone slowing down to 20mph so they can gawk at it. Then there is the inevitable shunts as someone forgets to brake in a line of traffic. Personally I would plant a hedge to shield view from the road. This in itself will make traffic flow better. Of course hedge will just not fit in with the Salisbury plain landscape. Stonehenge was put there originally for its long views of the horizon and the sun rising/setting.
Put down some gravel and pave a road. Any artifacts will be safer under the road than if dug up for a tunnel. If you dont want to see the road, box it in above ground. Plant hedges around it. Dont rip up history just because you dont want to spoil someone's view.