Are there units that produce 300” to 340” bulls that won’t take 20 years to draw?
Pretty much all of them produce 300-340 bulls. The question is whether you're okay with a late rifle tag versus holding out for something around the rut. If so, you can hunt 300+ bulls with a rifle every 5-7 years or so. The link attached should be to a free Epic Outdoors online mag, from January 2017, that includes AZ. When looking at the points, remember that you get two extra bonus points for (i) taking the AZ hunters ed class (half day if you're ever down there for vacation), and (ii) a loyalty point for applying five years straight. So if you apply for five years and take your hunters ed class in that time, you'd have seven points total. And then you get one in the draw, so you'd actually have eight total in your sixth year of applying.
https://epicoutdoors.com/epic-outdoors-magazine-issue/