The power supply you were originally using probably died because you were overloading it. If it really is a 300W amplifier (the ratings on some cheaper amps are somewhat generous) it will draw a lot more than 6A. At full output it will be drawing more than 25A (300W at 12V is 25A, but no amplifier is 100% efficient).
I wouldn't bother with the Jaycar power supply you listed. It's probably a switch mode and will just shut down when overloaded. Those old lab power supplies were built like tanks and would take almost any abuse and survive. A $40 power supply from Jaycar will not tolerate being overloaded.
A better option would probably be a PC power supply. Some have 30A 12V outputs and I've used them to run car audio gear before (for testing, never in a permanent installation).
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