The power output of common 445 nm and 640 nm diodes is not significantly affected by small temperature fluctuations. Fast control loops of any type are purposeless here, because the thermal mass of a typical diode mount acts as a big low-pass filter anyway. Fortunately, proportional control is perfectly sufficient for this application, does not risk overshoot or undershoot, and does not require tuning any loop parameters. I posted the schematic for a very simple proportional TEC controller earlier in this thread.
A PID controller like the one being discussed here would be appropriate for things like temperature control of DPSS crystals, which are sensitive to slight and rapid temperature fluctuations. Fast control loops are only possible with a small thermal mass, which is why the crystals are often nestled in indium foil directly on the TEC rather than using a bulky mount. I'm impressed by the open collaboration going on here and I think that the design so far is a valuable community contribution.