only the TLC is capable of PWM, right?
No.
A better option if you go down that route is the PCA9685, unlike the TLC chip it is a set and forget system, so requires much less software interaction. It still only controls 16 LEDs per chip but it is I2C with six address setting lines so you can have up to 64 chips on the I2C bus without resorting to tricks. You can get the chips on a break out board or solder the bare chip onto a carrier, like here:-
