I went back to using bipolar transistors and managed to make a circuit that could get up to 12 volts. I changed the output circuit to a darlington network to get more gain (hopefully.) The circuit was operating at an input voltage of 2.7 volts.
I tried switching to the 5-volt supply and I could comfortably get 12 volts into 220 ohms — 54 mA for a total power of 0.65 watts; with 51 ohms, I could get 8 volts or 1.3 watts. I'm pretty sure I'm up against the output capacity of the transistor at this point, so I tried a heat sink but it didn't help.
Anyway, in the process of digging around, I found this high-power NPN transistor. I hooked it up on the DC-DC converter and managed to drop 15 volts across a 51-ohm load with 5 volts in — a total of 4.4 watts. That's getting there.
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