Any horn speaker with horn honk is ether not properly designed or improper setup and partnering equipment. Your AN speakers are very nice, they have some of these horn characteristics, great dynamics, big sound, sense of performers in room, musical, probably my favorite box speakers, and one of the good ones regardless of design.
Horns will allow use of 300b, 2a3 or perhaps 45 tube amps, I do like Voltis, use his tractrix horns in my highly modified Khorns. Voltis are refined horns, they won't shout you out of the room.