The french company Online.net has some excellent and really cheap public root servers on offer. (Think: ten dollars per month for a full server with full root access). Unfortunately the selection of Linux distributions on offer (Debian, CentOS, Ubuntu LTS) doesn't include Slackware.
I did some experimenting and found a way to install Slackware64 14.0 on one of those machines. (Prior experience with LFS and Gentoo was helpful.)
Here's a detailed HOWTO on the subject. It's in French, but then again, the Slackware bits are universal:
Abstract: how to install Slackware using an Ubuntu Live session, and without a Slackware installation media. Bit of an ugly hack, but quite fun.