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There is a short term plan of including this kind of functionality in Akeeba Backup 3.1, in the form of a "Lazy scheduler" plugin for Joomla!. That said, here's how the WordPress plugin differs from Akeeba Backup.

AFAIK,the WP plugin you mentioned takes a partial backup, i.e. it excludes system files. Moreover, it tries to perform the ENTIRE process within a single page load. This is just plain impossible with Joomla! because the number and size of the files, as well as the amount of database information usually present in a Joomla! site is far beyond the capacity of what PHP can do within a single page load without timing out.

Akeeba Backup (ever since it was JoomlaPack 1.0 Beta back in October 2006) tried to effectively work around this restriction by "batching" the work in multiple page loads. This means that in order for your website to be backed up with the "Lazy scheduler" you need to ensure that enough hits on your site will occur in order for the backup to be complete. It also means that if the database backup needs several page loads to complete, you need a lot of hits on your site within a limited time frame to ensure that the database backup will not be inconsistent.

With all of the above in mind, I'd suggest taking a look at Akeeba Remote Control which is able to schedule a backup and download the backup archive to your PC (or let it upload to S3, whatever you prefer). The drawback is that you need to have your PC turned on for the backup to take place.

Alternatively, you can migrate to a decent, performance-tuned host, like Rochen. In fact, we convinced the guys at Rochen to offer a 20% discount on the first invoice if you use the coupon code "akeeba" during checkout. Rochen does support CRON jobs and works perfectly with the native CRON script (backup.php) and uploading the backup files to S3. This site is the living proof ;)