I was always under the impression that it’s not really possible to overdrive speakers that require high current to drive
This is in need of correction- you can overdrive any speaker if you have enough power!
Now i just want to research options for class D
I would certainly give them a try. Class D is different from regular solid state- its artifacts are not the same. There can be difficulties with low impedances on account of the output filter of the amplifier; you'll have to check with the manufacturer on that. But the low impedance at high frequencies may not be much of an issue as there is not nearly as much power up high.