That's the basic idea (no warranties expressed or implied). I'm assuming that the controller can dim the LEDs, and uses PWM to do it. If so, then the new FETs have to be fast enough to keep up. Might be a problem because a large MOSFET has a large gate capacitance, and needs a gate drive circuit that can charge and discharge it fast enough to keep the FET out of its linear region when the big current is flowing. I couldn't find a datasheet on the controller chip, so this approach is a bit of a gamble.
Before any mods, operate the controller for a while with 2A loads and feel the original FETs to see what the designers think a reasonable operating temp is. Then you'll have a starting point when the new FETs fuse your fingerprints.
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