I thought this was neat. I was going through the FAA permits for downtown and found a permit from 1987 for a 240 foot hotel on the northwest corner of the One American Center block. It would have occupied that vacant lot.
https://oeaaa.faa.gov/oeaaa/external...D=261275&row=5
Also I found a height for the Lamar Financial Savings Plaza. This was a project that was proposed in the early 80's that would have occupied the space where 300 West Sixth is. It has had a 12-story hotel with it. The office tower was 27 floors, and this height says it would have been 383 feet.
https://oeaaa.faa.gov/oeaaa/external...D=257370&row=5