I've only received monitors via UPS three times.
My 17" Nanao monitor arrived with with what looked like a forklift tine hole punched through the front of the box. Whatever it was nicked the plastic-wrap around the monitor, but did not damage the immediately contiguous monitor face. Pure luck that the monitor survived.
The second monitor was a 19" Mitsubishi Diamond Pro 900u. It was clearly obvious that this monitor had spent a fair amount of time outside of its case rolling around loading docks. It was severely scratched, scoured, and part of the case was broken off.
The replacement unit for the above 19" monitor arrived somewhat worse for the wear, but still intact. I have never completely succeeded in adjusting the picture on this one. No matter how hard I try at least some part of the picture is too wide/narrow when compared with the rest of the picture. This raises in my mind the question as to whether it was mistreated to the point that some of its internal elements are out of alignment.
In short, I am totally unable to recommend UPS on the basis of the experiences I have had with them.
It may just be a fact of life that there is no freight company that is worth a damn at this.
Whatever you do, you have my very best wishes!