The ticket type cannot be changed.
I just upgraded from 3.1.0 to 3.1.2. It's still not possible to change the ticket type.
If output_buffering (php.ini) is disabled, you get this warning and the rendering stops:
Warning: Cannot modify header information - headers already sent by (output started at /path/to/your/traq/vendor/traq/models/ticket.php:354) in /path/to/your/traq/vendor/avalon/http/request.php on line 176
If I enable output_buffering, then the page loads without a warning, the comment "Changed Type from XYZ to ABC" is posted to the ticket history, but the type of the ticket is still XYZ.