openGLCD works on Teensy 3.0/3.1 https://bitbucket.org/bperrybap/openglcd/wiki/Home
It doesn't use DMA but does use the slighty faster digitalXXXFast() routines.
Even though the Teensy 3 is clocked faster, pin i/o is faster on the AVR because of the way the i/o works.
On the AVR the code can set multiple bits in a single instruction, which can't be done on Teensy 3
