When my son went to Israel he went to work in the settlements... not to evangelize, just to work... That is the proper way IMHO. The locals say they 'can see Messiah' in folk like him.
Yes, they have excavated all the way. The part where the Cornerstone is exposed is not open yet to the public. I hope to be there when they do open it. They have found some amazing things, like a small amphitheater, a few more rich folk palaces, and many other things that they have not announced yet (I wish I could tell you.) The tunnel that I was in goes from the entry to the City of David, which is on the South Side of the street that enters through the Dung Gate (it is about 100’ below ground. It travels under the Archaelogical Park that is just south of the Temple Mount and the Cornerstone is about 90’ below the surface excavation where the top cornerstone was heaved off by the Romans in 70 CE. If you do go, it might be open now - I was there 4 years ago. They also found caches of gold (one place was about 350 pieces), which were no doubt placed there by “preppers” of the day. If you would like any other info, private message me.