Removing the old:
To mount the range/oven combination, I used some of the side trim at the bottom below the oven as there was about 1.5" of open space. Behind that, I put a piece of dimension 1x2 cedar wood all the way across the back (so braced by the rest of the structure). The oven has two screw tabs on the bottom and I used two long screws to go through the trim and into the cedar strip. So it's on there nice and solid.
Up top, I discovered on the old range they hand't screwed into the support wood beneath the counter. At about 1" down from the counter surface, there is some wood that is ideal for attaching the range. So I drilled some new holes in the new range/oven combo at that height and put in some screws on each side to secure it.