Update: Success!
You can indeed see the three tallest buildings in downtown Raleigh from Occoneechee Mountain. The visibility was just bad the last time I tried. So there you go. 33 miles. Is that the furthest? I believe we can actually go much farther.
Moore’s Knob in Hanging Rock State Park is 101.33 mi away at an elevation of 2,579 ft. There appear to be no hills or obstacles in the way. The 3 tallest buildings would be very small on the horizon, and could only be seen on a super clear day with a good zoom lens. However, I’m a bit more confident now that it can be done.