I did try reinstalling 7.1.1, and then when that failed again (with the problem noted above, I tried 7.1.2. But, in 7.1.2, it never completes the install, it stopped in its tracks while creating the tables in the database.
I found the log, and both errored the same way:
Wed Jul 23 00:55:19 2014 [29939][-none-][FATAL] Configuration variable date.timezone is not set, guessed timezone America/New_York. Please set date.timezone=“America/New_York” in php.ini!
So, I took the time to modify the file php.ini.
This stil has no effect. I changed the php.ini file exactly as the error suggests.
The weird part is that I have already installed SuiteCRM on this same server before with no problems.