I never attempt the Masuda method until both parent Pokémon already have 6x perfect IVs or 5x with the one missing being the toss-out stat (e.g. Attack for Modest/Timid natured Pokémon). It doesn't take that long in XY and ORAS with a 6IV Ditto.
I'm not sure what you mean by "wasting one egg per cycle." You have two perfect IV Pokémon at the daycare. One with a Destiny Knot to take care of IVs, one with an Everstone to take care of the nature. You see the first egg ready to be claimed. You save. You collect 5x eggs and hatch them. You don't see a shiny amongst them. You reset. Claim the first egg (different stats now). Collect 5x and hatch them. Repeat until you get a shiny.
It's much better soft resetting. You cannot recharge Hatching O-Power level 3 (costs 4 slots) fast enough by using it every batch. It takes approximately 3 minutes to hatch all 5x eggs in the party unless you're dealing with a Pokémon with a long egg cycle. It takes 4 minutes to restore a single O-Power slot. Resetting the game restores the O-Power gauge to its previous state. You really don't want to go without Hatching O-Power level 3. It literally cuts the hatch time in half.
Just to re-clarify, I meant resetting after each batch. You obtain 5x eggs, that's one batch. They all hatch, none of them are you want, you reset the game. Collect a new set of 5x eggs, repeat.
Once you talk to the daycare person and the egg enters your party, all the Pokémon's attributes are already determined. That's why you save before collecting the first egg.
What I meant about wasting the egg is that before an egg is generated, the game has already determined which parents will pass on which IVs, and what the throwaway IV will be. (E.g., baby will get M/M/F/F/F/X, where M is from the male parent (or Ditto, if the other parent is female), F is from the female parent (or Ditto, if the other parent is male), and X is randomly generated, but will be the same value for that particular egg every time.) So depending on when you've saved, you won't actually get different stats for the first egg every time you reboot, though I believe the chances of it being shiny will reset each time, since I think shininess is generated at a different time point than which IVs are being passed by which parent. IV passage is determined before the egg is generated (after the previous egg is collected, I guess), while shininess is determined when the egg is collected, I think. I'm not sure when ability is determined.
(The IV passage thing led to a trick early on where you could save, stick two Magikarp or a Magikarp and a Ditto with known IVs into the daycare as parents, quickly gather and hatch an egg, see what parent passed on which IVs, and then stick the appropriate male and female in to pass along the IVs you want. It's not that relevant now with perfect Dittos and such, but it can be helpful for breeding more unusual HP spreads and the like.) Depending on when you've saved, and when you're resetting from, the IVs passed on by each parent have already been set, and if you're using the same parents, you'll always pass on the same spread for that first egg (and then the remaining four eggs will vary). So for example, if you're going for a sweeper on a non-trick room team, but the game has decided not to pass along the speed IV, and the one the game generates is not 31, that first egg is always going to be garbage. This can work to your advantage, if you've saved at a point where the next egg generated will have a perfect spread for what you're looking for, though. It's been a while since I've tried out that method (I generally just brute-force breed now, and release everything afterwards), but I recall it working as described when I originally used it shortly after X came out.
The O power thing is a good point, though. I generally try to take a break every time I run out of level 3 hatching power, or use my other 3DS (which I reset without saving) to gift myself hatching powers.
And for some reason, I got ten notifications from your single quote of my post. Don't know why that happened...