I have searched the forum and found many references to fixing the /temp and /logs directories to be writable.
I have confirmed that httpd is running as apache:apache, setting the directories to 777 and chowning them to apache:apache still doesn't correct the error in the installer.
Putting SELinux into permissive mode temporarily does solve the problem, so I'm sure it's related. Further reading on SELinux would indicate that it's because the directories don't have the correct security context maybe?
I'm getting in really deep at this point for my level of noobiness.
Has anyone else solved this?