I talked with one of the workers this morning and they are working hard to get it closed in. They aren't waiting around because of the heat and they should be totally closed in in about a month he said.
Apparently the Chase Apartments next door to the Chase Hotel on Lindell is going to be remodelling all of the suites (~200) at some point and he did allude to the start of construction on the Renaissance, but he didn't know a timeline, but the Subway has got their sign up across the street now. Once they've moved out I think preparations for demolition of the Doctor's Building can go ahead.
It also looks like PicPile has officially given up the ghost so the old updates I had placed may not be visible anymore. If they are indeed gone, I'll try and edit my posts down so the pages load in a reasonable time again or replace the images on photobucket, but I might not remember all the views, so I'll probably trim them up a bit.