well, i´m not sure, if i can help you, but it looks like a hardcore-crash course>>if you are new to electronics and wanna tweak the TLC5940. unfortunately, i don´t have experience with it, but i guess you can limit your errors a bit. or boil the problem down: easily said, you will need 16 12-bit "packets" because it will shift the input with a 192-bit width after a rising edge of XLAT (10ms should be enough). then next 192bit through Sin. i´m not sure, if you really need to use BLANK, cause it´s never mentioned in the timing diagrams. just put it to GND.
you should use delays between HIGH and LOWs, otherwise the IC is not capable to detect a raising or falling edge!
and increase the size of R(iREF). it is responsible for output current. if you have ordinary LEDs, you can easily take a 1,9kOhm resistor, as you will have 20mA on each output.
Hopefully, there are other users who experimenting with TLC5940, as for me it is unclear, if you can talk to it with SPI, or the serial interface just looks like an SPI interface. if so, where is Chipselect?!
good luck!