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It definitely was the MOSFET! Everything's working as it should!
I went ahead and ordered the same MOSFET that you used so hopefully that's it. I soldered the parts to an Adafruit Perma-Proto HAT and right now the LED strips are only getting 7.2 volts but if I put the multimeter leads between the hot where the LED strips connect and the standard ground it's the full 12 volts. I'll report back on the result.