All the values relating to the baby Pokemon are decided when the egg is created, when you accept the egg from the Daycare Helper. Nature, IVs, Egg Moves, Ability, everything. Saving after this point will not help in anyway, you must save before it. For this reason, soft-resetting is not an effective method for your purposes.
As for passing HAs, one of the parents must already have the HA for the babies to inherit. If breeding with different species, this means the mother is required to have the HA, as the mother determines which specie. The mother has an 80% chance to pass down HA, the father when same specie has a 20% chance to pass down HA.