To get an giant owl from a regular owl, you throw away the regular owl entirely and make the giant owl as a fresh creature from scratch, based on the idea “giant owl.” There's no modifying involved; they're completely separate creatures, built separately from the ground up to best fulfill the creature concept you have.
So skip past “Modifying a Monster” on page 273 and move along to “Creating a Monster Stat Block” on page 275, with a brief stop at “Creating Quick Monsters Stats” on page 274 (since the full creature-creation rules reference that section).
Clarifications of a few details you bring up:
Since the Giant Owl and the regular Owl are, as far as mechanics are concerned, completely different and unrelated creatures, the attributes and other statistics are equally unrelated and no amount of trying to discern a pattern will be fruitful. Instead, they're pretty much chosen arbitrarily, to fulfill the creature's concept, and that's what you should do for your Giant Ape. See “Step 5. Ability Scores and Modifiers” on page 275.
Similarly, bonuses and attack damage are either arbitrarily chosen, calculated like PCs' bonuses and damage are, or are based on its CR using the table on page 274.
The hit die type is based on creature size, but the number of dice has nothing to do with its “level” (creatures don't have levels). The number is chosen either so that the average HP that result match the expected HP for its CR, or just arbitrarily to fit the creature's concept. See “Step 8. Hit Points” on page 276.
Alternatively, you can leverage the rules for modifying monsters, if you start from the right kind of monster. Forget about what the concept is — just find a monster that's already similar mechanically to what a gorilla would be like. How about a hobgoblin, or a gnoll? Those are both strong, big humanoids and might be close already to what you want from a gorilla. Now use the “Modifying a Monster” rules to take away its language, weapons, and any special abilities that don't fit, and make sure it has a slam attack and a bite and you've got something gorilla-like.
Keep in mind that even the official monsters are not made out of a formula — they're roughly based on these guidelines, but what looks good on paper may work very differently in practice, and it's how they work in practice that matters above all. Take the example of the ogre: it's CR 2 instead of the expected CR 1 simply because it's more powerful in play than what the monster-creation rules would lead one to believe. When in doubt, compare your creation-creation results with the creatures in the Monster Manual to get a rough idea of whether the result is good, and whenever possible, test them in play.