A cheap component would have poorere Rth die-case, which wouldn't change the dissippation (unles it dissipates itself directly to ground, which would be very weird), and if anything it would lower the case temperature (but raise the chip temperature). What exactly do you mean by overheating? Too hot to touch? Or does it thermally shutdown?

You realise the Arduino is none of the above? It is an IDE and a library, targeting a wide range of hardware boards, some of which are also called Arduino. If you refer to the Arduino Uno, that is a board (PCB) with a specific micro-controller.

Another experiment I'd try: with the lonng distance, power the LED strips from the far end with an independent power supply.

Another experiment: use RS485 to transmit the signal. This should be much less suceptible to ground currents.

You mention 3 A with all LEDs fully on. That is much less than the 5.1 I calculated. This is something worth investigating. Does the problem remain with less LEDs (let's say 10) but still at the long (8 m) distance?

If you think the length of the signal line is the problem you could try the 8 meter line with single ws2811's each let's say 0.5 meter as signal re-shaper.