Drupal 6 to Pressflow migration: MyISAM to InnoDB?
You should be fine going from Drupal 6.19 to Pressflow 6.22 but make sure you backup files and database just in case.
As for converting the tables your best doing that either through mysql cli, or phpmyadmin.

I would treat these as two separate jobs: First, migrate to Pressflow and confirm the site is working; then, secondly, start moving tables.