My problem is the extension. These are speakers that should be capable of going truly full range and diving below 20hz. But they're not getting there. I actually have a subwoofer and it is here that I notice the missing depth. But I want the speakers to go full range without the subwoofer.
It has probably more to do with your room (what are the dimensions, L,W,H?). Most high quality amplifiers should measure flat between 20-20,000 Hz at less than 0.05% THD+N. For more power, I wouldn't go with those hand make class D amps and go with the try and true well known amps that have good specs verified by available 3rd party lab measurements.
If you don't mind paying more, you can choose one that is rated 300-500WPC from Bryston, Classe, McIntosh, Passlab, Parasound Halo JC mono blocks, Hegel H30 etc., or for a little less, something like the ATI6002 will be more than good enough for the 802 D3. If you don't mind spending less than the Crownaudio pro amps suggested should be fine too.
By the way, looking at the frequency response of the 802 D3 in the anechoic chamber, I would not consider them full range. For them to be full range, it will again, depend on your room.