Here's a very rough schematic for a very rough circuit. Due to VGs being around 4V, I have to run this circuit at ~7.2V to get any real current from the mosfet. I don't do this long, I doubt there's a heatsink big enough!

I am familiar with a wide range of micros, I've built a few PCBs that actually work. My latest contains a 328PB that reads serial data from a wideband controller, data from a 3 axis accelerometer, a MAX31855 for EGT and a few ADCs. It sends all this data to an aftermarket ECU in realtime via a custom canbus protocol. I built a logic analyzer from a cypress chip and sigrock, I wrote my own bits of code for serial data from the wideband controller, the thermocouple over SPI, and the accelerometer via i2c. I tried to leave enough space to run a OLED display I made that fit in place of useless instrument cluster gauges, but RAM is too tight and I only halfway know what I'm doing to fix that! I need to move from the MCP2515 library and write more dedicated code, but still don't think it'll be enough. I have another more complicated board that uses a teensy 3.6 that runs that display great, though! I've enough knowledge to map pins on that thing, plus use a few of the modules like the FTM to read wheel speed sensors in a language ECUs understand, although that's cheating as much work as Paul's put into that whole kit.
I think I can handle the microcontroller part, and would probably build a custom board that ran on a 328PB since they're so dang cheap! I might try and seed the TEC current PID control by reading an average of the last analog voltage that relates to laser output power, plus I'd be able to shut the laser off completely if either the hotside heatsink or coldside diode got too hot. All of this is going into a custom built laser projector, so I'll have three of these little TECs to drive. I'd like to do it independently, mainly because I want to run the red diode as cold as I can while the other diodes can stay at room temperature. I'd also run a fan off a little PWM circuit, to keep the hotside cold and quiet as possible.
Since I'd like to make this a compact projector, I'd like to avoid large inductors for filters. I don't know squat about analog, but I've ran a few online calculators and think I'd need quite large inductors right, if I wanted a smooth 3-4V to power a mosfet? I guess low setting time won't hurt much in this application, though, can I just use a large capacitor instead?
The TEC I am using is a 12x12mm TES1-1704, described as 4A max and Vmax of 2.05V, TC max of 67c, QCmax of 4.8W. The block these TECs will be cooling is a small lump of brass, 12x12x15mm. The hotside will be a relatively large aluminum plate, with a finned extruded heatsink mounted underneath. I think this arrangement should work well, and shouldn't stress these TECs too hard. Another reason I'd like to avoid unfiltered PWM or worse bang-bang is because these TECs will be under laser diodes, I've seen what bang-bang does to 3d prints and I don't want anything like that with my laser alignment!!
I've ran these things off a constant current bench supply using massive aluminum plates for heatsinks to try and maintain equal temp on both sides of the plate. I've measured the operating voltage to be around 0V to ~2V at 2A. At 4A, they jump to 3.6V. I am not sure how this changes with temperature, but I am sure it does.
Also, a mosfet should be able to switch voltages lower than the control signal right? Within reason of G-S ratings, at least? So if I manage to build a switching supply that runs much closer to 2V, my mosfet won't waste as much heat, letting the more efficient switching supply do that.
I also have no real reason to use a IRF540 other than I have some here, either!
Thanks for reading everyone, and for the tips! Sorry for writing a book!