I was finally able to install both SwiftRiver and Sweeper at the least likely place: Siteground. They have an option to switch from the default PHP 5.2.9 to 5.3 or 6.0, either for the whole site or a particular directory.
I installed SwiftRiver on a subdomain and then switched that particular directory to PHP 5.3, proceeded with the installation and all went without a hitch until the very end, where instead of being taken to Sweeper, I got a 500 error and "in addition" a 404 error.
Checked database credentials, .htaccess, etc and all is fine.
Deleted SwiftRiver and created new directory for Sweeper, on new subdomain. Same exact thing.
Is the subdomain causing the problem? I cannot install at the root due to the main domain being a WordPress site. It must be a subdomain. (I can't install at the same location as WP because that part of the site is at Bluehost, which doesn't support PHP 5.3...)