I found a FAA filing for a "24-story hotel" at Lat 30° 16' 08.75" N and Long 97° 44' 37.01" W
If you enter those coordinates into Google Earth, it pinpoints the location as being on the northwest corner of the block where the One American Center is.
This was a filing from May 14, 1984. It lists Rust Properties as the sponsor. They're the company that developed the One American Center.
https://oeaaa.faa.gov/oeaaa/external...=253241&row=20