Now that I knew what voltage and amperage I needed, I ordered a power supply from Amazon. What I got was a dead 24V 5A power supply :(

After returning it, I decided to go a different route. I've been interested in USB PD, and after some searching I found a PD trigger cable that requests 20V and has a simple barrel plug on the other end. Just pair that with a USB C power supply capable of 65W and everything should work. Running the lamps at 20V is less heat, but I tested it with my bench power supply and it seemed adequate. The current draw was also reduced to 1.5A which means 60W total. This should work! I also got a cheap LED dimmer so that I could control the heat. This turned out to be a crucial element later.

I tested this power supply with a single lamp and it didn't work...

I grabbed my multimeter and the reason became clear. The power supply initially supplies 5V, then after the PD chip negotiates, it supplies 20V. The problem is that the lamp is essentially a short until it heats up. It doesn't take long for it to heat up, but it's still enough to make the power supply shutdown.

So I put the LED dimmer in-line and slowly turned it up. This gave the lamp time to heat up before the voltage got so high that it tried to draw too much current. So as long as I always turn it on slowly, it works. I can live with that.