As I pointed out earlier, size changes alters your base damage to a new base damage. A 1 step size increase makes a medium dagger into a large dagger dealing d6 base damage. Bashing does the same thing by increasing the base damage by 2 sizes to a new base damage.
I understand where you're coming from, and at my tables, I would rule in your favor, because I feel that this is how the rule is intended to work.
However, without an FAQ, we're left with interpretation based on the rules as they currently exist. The only reference I can find that specifies that increasing a weapon's "effective" size altering it's base damage is in the spell description for Strong Jaw. Even Gravity Bow and Lead Blades talk about increases the weapon's damage as if it were a size category larger - base damage is not mentioned. If you could link an FAQ or show where in the rules it states specify that magical augments to "effective" size of a weapon increase a weapon's base damage, it would help.
Close Combat Master specifies that the only affects "base" damage, you still use every other aspect of the weapon. Like, if your shield is made of Cold Iron or Adamantine, you'd still overcome applicable DR, but be using unarmed damage (a level -4) to do so.
Which brings up the question, how does Strong Jaw interact with Close Combat Mastery?