I actually am not a fan of RNGing anyway, especially considering you can easily get 5IV (and even 6IV) with little effort. I have 6IV Ditto, so it's extremely simple to get 5IV by breeding a batch of 6-12 Eggs, picking the best IV candidate and leveling it a little if you want to preserve Egg Moves, and then inbreeding it with Ditto (give someone a Destiny Knot, and if you want a certain nature you can pluck that out instead and work it in with a little more time using an Everstone) and repeating the process. Sometimes, you can luck out on a 5IV in the first batch; sometimes it takes two or even three batches. From there, it's all about luck as 4IV becomes the lowest possible (the one missing stat being selected can cause that, and that stat will always not be 31 in those cases), 5IV is most frequent (if 5 31s get selected, but can also involve the missing stat and a random 31 in the 6th stat), and 6IV is a combination of good IV selection and luck. I have over a dozen 6IV that I've bred myself (non-Shiny, and many by accident, one from a 4IV parent!), and haven't done more only because I took a break from breeding.
So, basically, once you get a 6IV subject, you can just level it up to the point it no longer learns moves, then (optionally for nature) hand it an Everstone while Ditto (likely not your OT) holds a Destiny Knot, and pump out Daycare babies. 5IV is a guaranteed result, 6IV is the luck factor. When a Shiny comes, see if luck strikes.
It's so easy to get good Shinies without RNG now. You just need the time. :)