You nailed it. It's not that easy.
URL redirection, or trying to get Joomla to work with Textpattern URLs, or letting the server rewrite those Textpattern URLs is the easy bit.
The 2 databases will be quite different. Tables, table layouts, row and column attributes, stored user profiles and passwords, categories, tags, articles, posts, pages, comments. It will all have to be converted.
You either write your own SQL queries and/or scripts, or you pay up. I think that a conversion service starts with just $100. But they will up the price quickly depending on the number of users+passwords, articles/posts/pages, permanent URL redirects (301), etc. But your site will be converted in 3-5 days.
Just make up your mind.
Service : google a database migration|conversion service +"textpattern to joomla"|+"mysql to mysql", gconvertor.com (payed) springs to mind.
DIY : Use tools like MySQL Workbench (free), DBConvert (payed), or Altova MapForce (payed).