Those MP Rotators that @robertokc recommended are a thing of beauty relative to my old heads. I have an odd shaped lawn as well and it was nice to be able to make fine increment angle adjustments, and +/- 25% throw adjustments, yet maintain the same pr. For that matter you could change from a MP1000 to MP2000 to further extend throw adjustment, and keep the same pr. Having said that,I certainly understand the pooch issue, which I don't have since he uses the back yard with a small patch of artificial turf.
Thanks for your info. I have 4 cycles of 33 minute each, for a total of 132 minutes. Divide that by the 3.8x difference in our precipitation rates and I would be at 35 minutes with the same pr as you. I'd say we're matched up! FYI, with 30 minute soaks in between the 33 minute watering, it takes 3.7 hours to complete my full cycle. You'd have to start quite early and your pooch would likely come back in with wet paws. Thanks!