Perhaps I mis-stated my intention, and I'm sorry if it gave you the wrong impression.
I don't mean to start climbing antennae to get to any highpoint. Certainly, there are structures that are not meant as a public standing place that may be higher than the official (land) highpoint; but this is crossing the "public accessible/standing platform" line.
What I've done is find a city's mean height above sea level (MSL) and added to that the height of it's tallest building. If that comes out to be the highest point in the state, then fine, I'll take it IF (and only if) the land highpoint is inaccessible.
So Delaware would still be in the trailer park; LA would still be on Driskill, but Florida and Illinois would have alternates in Miami and Chicago respectively. In Indiana, take your choice, a little rise in the outback of the state or the highest floor of the tallest building in Indianapolis...