Running DC DC converter at max. rated amperage
You should not use the 12 V, 2.5 A supply as it cannot be expected to deliver 12 V at 3A reliably. Sure it might work for a while but there is a change it will slowly deteriorate (damage) when you constantly overload it like that.

Indeed the LM2596 is rated for a 3 A maximum output current but loading it with 3 A also means that there is no margin. In engineering, that's always a bad thing. And here it is easily solved, get a 5 A DCDC converter.

However converting 14 V to 12 V at 3 A is on the edge of what most DCDC converters can do, the voltage difference is quite small.

I would examine the board which needs this 12 V, 3A and see if it has any on-board regulators. If it does I would use a couple of diodes in series to drop the 2 Volts. You will need a lot of diodes though or a few "beefy" ones as they would need to drop 2 V at 3 A which is 6 Watt.

Also 12 V 3A is 36 W, which is a lot of power. The board might actually use a lot less power but you would have to measure that to confirm.