If both of these possibilities are small, is there a better way of going about this?
Well, of course, the answer is yes!
The fastest way to max the IVs of a certain Pokemon is to have a 6 IV Ditto, and have it hold a Destiny Knot in the Daycare. The Destiny Knot is an invaluable item for any breeder. If either of the 2 Pokemon is holding it, the child is guaranteed to inherit 5 of it's 6 IVs from one of it's parents, chosen at random. Every time you produce a child with more IVs than it's not-Ditto parent, you replace that parent with the child, and repeat the process. Eventually you will get either a child with 5 IVs in the stats you care about, or a child with all 6 IVs, which is the first step in breeding a competitive grade Shiny.
Similarly, the Everstone allows the Pokemon holding it to pass it's Nature down to the children, instead of the Nature being chosen at random. I usually get this step out of the way before worrying about IVs, because you just move the Everstone from parent to child when you swap them in the daycare. The Ditto is holding the Destiny Knot, ensuring you get both the correct Nature and your crack at improving the IVs of the children.
So, the question becomes.... How do you get a 6 IV Ditto?
/r/BreedingDittos will give anyone a 6 IV Ditto holding a Destiny Knot, usually Shiny, once for literally free. Whats more, if you are interested in Shiny Breeding, they make an effort to ensure the Ditto they give you is of a different language than your game, ensuring you get the benefits of the Masuda Method, increasing the chance of hatching a Shiny. They do have a lot of rules and requirements you have to meet, but it is worth every second of effort. Beyond that, there are occasionally giveaways hosted by contributors to the sub, allowing you to get additional 6 IV Dittos. One of the giveaway peeps in particular is known for also offering Trick Room Dittos, as well as a limited variety of Hidden Power Dittos.
