The 12V version works as expected. It can provide nearly 20A of current to the handpiece/tip without any significant problems (except maybe temperature rise.)

The 12V PCBs arrived from OSH Park around 2025-01-025 -- more than one month after I ordered them on 17, December, 2024. They had some issues with their suppliers. But the PCBs worked and I assembled them. There's not much so say other than they worked as expected. I took some measurements of power dissipation and efficiency:

The handpiece and tip resistance was measured (with a 4-point resistance probe) to be: 0.0984 Ohm. (that is with a 18AWG Nichrome tip). 

When I applied 1.421V across the handpiece/tip it required 2A from the supply. Therefore, the efficiency of the burner is around 85.7%. Switched-mode converter aficionados might poo-poo this number, but most of it is wasted in the power dissipation of the 6.25mR sense resistor used to detect peak output current. This is consistent with expectations from simulation.

I placed a temperature probe over the top FET, Bottom FET, and sense resistor string and got these results:

Top-FET: 41C

Bot-FET: 45C

Rsns: 53C

This is consistent with expectations from simulations as well. The sense resistors dissipate higher power and therefore will have higher temperatures. Extrapolating the temperature/W readings from the measurements gives a 30C/W thermal resistance number for the resistor string. That's pretty good! But when the dissipation of the handpiece approaches 50W, the expected temperature rise will be around 70C, which is pushing it for a 3D-printed enclosure.

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Real world testing indicated something entirely different. When the burner had a current of 15A flowing through the tip, as the tip contacted the piece of fir it would "explode" into a flame with a sudden "pop". It was a lot worse when the current was 20A. It appears that I have over designed the wood burner. But that is easily corrected with an adjustment of the trim pot for max current. In the future, I will be adjusting the max current available to the tip to align with reality.