My congratulations on a very clearly explained test on what figures represent on the amplifier, and everything else.
There's an easy thing I would recommend to anyone buying any of these class D amplifiers, probably whichever the chip is. Unscrew the heatsink, clean the thermal grease, which might probably be dry (that happened to on a Breezy Audio amp), and replace with the white thermal grease you can buy for a few dollars. Just a thin even layer all around the chip. That should improve heat dissipation a lot!
You can always try to find another heatsink that is longer, or taller, though taller would make impossible using the box top cover, except if you cut a hole around the heatsink fins.
Another thing you could try is using a small fan, though that may make noise.
Replacing the grease can be done by anybody. For the rest you need some more experience in DIY mods.
Space will probably not allow it, but you could move the large "Nichicon" caps below the pcb and increase their size at the same time, to 2200uF or higher. The higher the better. Or you could move toe caps with wires to the vacant space below (on the internal pcb picture that was shown) and lie the caps horizontally, which would also allow higher capacity caps. You have to add two 100nF film capacitors to the pads you took the caps from.
Some people in DIYAudio have modified many other parts, but these things I described are things that demand little work. Once again, this should be done by people that have electronics DIY experience.
Well, just my five cents.