Increasing voltage regulator current
The change you're considering looks like it doubles the number of parts in your circuit. Those new parts will be getting hot too, so bodging them onto your board isn't really possible for long-term reliability, they could do with decent heatsinks.

Unless you really do have to keep your 78xx regulator, I'd strongly recommend you change your design to a higher-current linear regulator or preferably a switching regulator.

That way, you'll have a single output stage rather than the half-transistor half-regulator circuit you were looking at. And that single output stage will have all the protection benefits of your chosen regulator: short-circuit, under/over-voltage, over-temperature etc.

If you want to really simplify things but spend more, you could use a DC-DC 'brick': a pre-assembled module with heatsink.