There is a method to speed up communication
In Adafruit_ST7735.cpp search for
SPI.setClockDivider(SPI_CLOCK_DIV4);
and change it to
SPI.setClockDivider(SPI_CLOCK_DIV2);
That will speed up SPI bus
I was using it on 3.3v 8mhz atmega328p, not on 16mhz so it may not work