@Paul, I just downloaded the optimized-IL9341 library and it doesn't want to compile, I am compiling on a PC-Win 7. I tried the original by Adafruit and compiles, and runs on the Teensy 3.1. I haven't tried to debug the library beyond what it's obvious on my setup and I wanted to check if you have seen this compile error:
Arduino: 1.0.5-r2 (Windows 7), Board: "Teensy 3.1"
C:\Users\coder\Documents\Arduino\libraries\ILI9341_t3\ILI9341_t3.cpp: In member function 'void ILI9341_t3::setAddrWindow(uint16_t, uint16_t, uint16_t, uint16_t)':
C:\Users\coder\Documents\Arduino\libraries\ILI9341_t3\ILI9341_t3.cpp:47:6: error: 'class SPIClass' has no member named 'beginTransaction'
C:\Users\coder\Documents\Arduino\libraries\ILI9341_t3\ILI9341_t3.cpp:47:64: error: 'SPISettings' was not declared in this scope
C:\Users\coder\Documents\Arduino\libraries\ILI9341_t3\ILI9341_t3.cpp:50:6: error: 'class SPIClass' has no member named 'endTransaction'
C:\Users\coder\Documents\Arduino\libraries\ILI9341_t3\ILI9341_t3.cpp: In member function 'void ILI9341_t3:

ushColor(uint16_t)':
C:\Users\coder\Documents\Arduino\libraries\ILI9341_t3\ILI9341_t3.cpp:55:6: error: 'class SPIClass' has no member named 'beginTransaction'
C:\Users\coder\Documents\Arduino\libraries\ILI9341_t3\ILI9341_t3.cpp:55:64: error: 'SPISettings' was not declared in this scope
C:\Users\coder\Documents\Arduino\libraries\ILI9341_t3\ILI9341_t3.cpp:57:6: error: 'class SPIClass' has no member named 'endTransaction'
C:\Users\coder\Documents\Arduino\libraries\ILI9341_t3\ILI9341_t3.cpp: In member function 'void ILI9341_t3::drawPixel(int16_t, int16_t, uint16_t)':
C:\Users\coder\Documents\Arduino\libraries\ILI9341_t3\ILI9341_t3.cpp:64:6: error: 'class SPIClass' has no member named 'beginTransaction'
C:\Users\coder\Documents\Arduino\libraries\ILI9341_t3\ILI9341_t3.cpp:64:64: error: 'SPISettings' was not declared in this scope
C:\Users\coder\Documents\Arduino\libraries\ILI9341_t3\ILI9341_t3.cpp:68:6: error: 'class SPIClass' has no member named 'endTransaction'
C:\Users\coder\Documents\Arduino\libraries\ILI9341_t3\ILI9341_t3.cpp: In member function 'void ILI9341_t3::drawFastVLine(int16_t, int16_t, int16_t, uint16_t)':
C:\Users\coder\Documents\Arduino\libraries\ILI9341_t3\ILI9341_t3.cpp:76:6: error: 'class SPIClass' has no member named 'beginTransaction'
C:\Users\coder\Documents\Arduino\libraries\ILI9341_t3\ILI9341_t3.cpp:76:64: error: 'SPISettings' was not declared in this scope
C:\Users\coder\Documents\Arduino\libraries\ILI9341_t3\ILI9341_t3.cpp:83:6: error: 'class SPIClass' has no member named 'endTransaction'
C:\Users\coder\Documents\Arduino\libraries\ILI9341_t3\ILI9341_t3.cpp: In member function 'void ILI9341_t3::drawFastHLine(int16_t, int16_t, int16_t, uint16_t)':
C:\Users\coder\Documents\Arduino\libraries\ILI9341_t3\ILI9341_t3.cpp:91:6: error: 'class SPIClass' has no member named 'beginTransaction'
C:\Users\coder\Documents\Arduino\libraries\ILI9341_t3\ILI9341_t3.cpp:91:64: error: 'SPISettings' was not declared in this scope
C:\Users\coder\Documents\Arduino\libraries\ILI9341_t3\ILI9341_t3.cpp:98:6: error: 'class SPIClass' has no member named 'endTransaction'
C:\Users\coder\Documents\Arduino\libraries\ILI9341_t3\ILI9341_t3.cpp: In member function 'void ILI9341_t3::fillRect(int16_t, int16_t, int16_t, int16_t, uint16_t)':
C:\Users\coder\Documents\Arduino\libraries\ILI9341_t3\ILI9341_t3.cpp:117:6: error: 'class SPIClass' has no member named 'beginTransaction'
C:\Users\coder\Documents\Arduino\libraries\ILI9341_t3\ILI9341_t3.cpp:117:64: error: 'SPISettings' was not declared in this scope
C:\Users\coder\Documents\Arduino\libraries\ILI9341_t3\ILI9341_t3.cpp:126:6: error: 'class SPIClass' has no member named 'endTransaction'
C:\Users\coder\Documents\Arduino\libraries\ILI9341_t3\ILI9341_t3.cpp: In member function 'uint8_t ILI9341_t3::readcommand8(uint8_t, uint8_t)':
C:\Users\coder\Documents\Arduino\libraries\ILI9341_t3\ILI9341_t3.cpp:211:9: error: 'class SPIClass' has no member named 'beginTransaction'
C:\Users\coder\Documents\Arduino\libraries\ILI9341_t3\ILI9341_t3.cpp:211:67: error: 'SPISettings' was not declared in this scope
C:\Users\coder\Documents\Arduino\libraries\ILI9341_t3\ILI9341_t3.cpp:255:9: error: 'class SPIClass' has no member named 'endTransaction'
C:\Users\coder\Documents\Arduino\libraries\ILI9341_t3\ILI9341_t3.cpp: In member function 'uint16_t ILI9341_t3::readPixel(int16_t, int16_t)':
C:\Users\coder\Documents\Arduino\libraries\ILI9341_t3\ILI9341_t3.cpp:263:9: error: 'class SPIClass' has no member named 'beginTransaction'
C:\Users\coder\Documents\Arduino\libraries\ILI9341_t3\ILI9341_t3.cpp:263:67: error: 'SPISettings' was not declared in this scope
C:\Users\coder\Documents\Arduino\libraries\ILI9341_t3\ILI9341_t3.cpp:282:9: error: 'class SPIClass' has no member named 'endTransaction'
C:\Users\coder\Documents\Arduino\libraries\ILI9341_t3\ILI9341_t3.cpp: In member function 'void ILI9341_t3::begin()':
C:\Users\coder\Documents\Arduino\libraries\ILI9341_t3\ILI9341_t3.cpp:314:10: error: 'class SPIClass' has no member named 'pinIsChipSelect'
C:\Users\coder\Documents\Arduino\libraries\ILI9341_t3\ILI9341_t3.cpp:315:18: error: 'class SPIClass' has no member named 'setCS'
C:\Users\coder\Documents\Arduino\libraries\ILI9341_t3\ILI9341_t3.cpp:316:32: error: 'class SPIClass' has no member named 'setCS'
C:\Users\coder\Documents\Arduino\libraries\ILI9341_t3\ILI9341_t3.cpp:344:6: error: 'class SPIClass' has no member named 'beginTransaction'
C:\Users\coder\Documents\Arduino\libraries\ILI9341_t3\ILI9341_t3.cpp:344:64: error: 'SPISettings' was not declared in this scope
C:\Users\coder\Documents\Arduino\libraries\ILI9341_t3\ILI9341_t3.cpp:355:6: error: 'class SPIClass' has no member named 'endTransaction'
C:\Users\coder\Documents\Arduino\libraries\ILI9341_t3\ILI9341_t3.cpp:358:6: error: 'class SPIClass' has no member named 'beginTransaction'
C:\Users\coder\Documents\Arduino\libraries\ILI9341_t3\ILI9341_t3.cpp:360:6: error: 'class SPIClass' has no member named 'endTransaction'
C:\Users\coder\Documents\Arduino\libraries\ILI9341_t3\ILI9341_t3.cpp: In member function 'void ILI9341_t3::drawLine(int16_t, int16_t, int16_t, int16_t, uint16_t)':
C:\Users\coder\Documents\Arduino\libraries\ILI9341_t3\ILI9341_t3.cpp:555:6: error: 'class SPIClass' has no member named 'beginTransaction'
C:\Users\coder\Documents\Arduino\libraries\ILI9341_t3\ILI9341_t3.cpp:555:64: error: 'SPISettings' was not declared in this scope
C:\Users\coder\Documents\Arduino\libraries\ILI9341_t3\ILI9341_t3.cpp:596:6: error: 'class SPIClass' has no member named 'endTransaction'
C:\Users\coder\Documents\Arduino\libraries\ILI9341_t3\ILI9341_t3.cpp: In member function 'void ILI9341_t3::drawRect(int16_t, int16_t, int16_t, int16_t, uint16_t)':
C:\Users\coder\Documents\Arduino\libraries\ILI9341_t3\ILI9341_t3.cpp:602:6: error: 'class SPIClass' has no member named 'beginTransaction'
C:\Users\coder\Documents\Arduino\libraries\ILI9341_t3\ILI9341_t3.cpp:602:64: error: 'SPISettings' was not declared in this scope
C:\Users\coder\Documents\Arduino\libraries\ILI9341_t3\ILI9341_t3.cpp:608:6: error: 'class SPIClass' has no member named 'endTransaction'
C:\Users\coder\Documents\Arduino\libraries\ILI9341_t3\ILI9341_t3.cpp: In member function 'void ILI9341_t3::drawChar(int16_t, int16_t, unsigned char, uint16_t, uint16_t, uint8_t)':
C:\Users\coder\Documents\Arduino\libraries\ILI9341_t3\ILI9341_t3.cpp:850:7: error: 'class SPIClass' has no member named 'beginTransaction'
C:\Users\coder\Documents\Arduino\libraries\ILI9341_t3\ILI9341_t3.cpp:850:65: error: 'SPISettings' was not declared in this scope
C:\Users\coder\Documents\Arduino\libraries\ILI9341_t3\ILI9341_t3.cpp:880:7: error: 'class SPIClass' has no member named 'endTransaction'
Thanks,