@erikt
You haven’t mentioned your cables, please share your interconnect and speaker cable lineup.
I owned the AN-K/SPx several years ago or as the Audio Note camp calls them, the Super K’s. A terrific speaker and very easy to drive. What is it truly that you are trying to accomplish tonally? Are you looking for more transparency? Decay like when a guitar string is plucked? What size is your room? How do you have the Super K’s placed in the room? Are you bi-wiring or using jumpers and if so, what kind of jumpers? What volume levels and what kind of music do you prefer?
There are many amps that will mate well but some of the suggestions above may not be optimal. There is also an incredible amount of performance potential from that speaker you have yet to hear. While the Luxman is a fine amp, it would not be an ideal match in my opinion.